I'm using this textbook for a first year PhD Introduction to Econometrics class and I'm enjoying the clear presentation, rigorous treatment and elegant typesetting. (The text includes Mathematica code on which I can't comment at this time, but the inclusion of code in such a text is encouraging in itself.)

the book was delivered in a few days and the condition of the book was good.

This text is quite good, with numerous examples, but beware of the many errors or cases of sloppy reasoning. A sampler:

p. 319. The maximum likelihood estimator for the binomial distribution, unknown number of trials, is unique. Not true: n=2, p = .4, sample = (1,6) is a counterexample.

p. 265. If S is the sum of k idd uniform (0,1) random variables, then Prob(S <= t) is t^k over k!. Not true: this would give prob(S <=k) > 1.

p. 62, 82, 84: Moments are unique (or non-unique). Nonsense, it is the pdf's that are unique or non-unique.

p. 444. Method to find a shortest pivotal interval. This is a non-proof. Apparently the authors haven't heard of Lagrange multipliers.

Note also that apparently there's no source for problem answers. This may or may not be considered a drawback.

I think this book is ok, at least for the first 4 chapters. You can self study through those chapters, as long as you have the solution guide, easily found online. However, some of the solutions are wrong so I would advise you actually work the problems. Chapter 5 unless you have a strong foundation in analysis and proofs, there is no way to understand convergence in distribution and probability. So I would go and get Casellas "A Probability Path" to get through that section. The second half of the book I have not read, but I imagine it only gets more into proofs and theory. DO NOT HOWEVER BUY THE CRAM 101 TEXTBOOK OUTLINE they are SUCH A WASTE OF MONEY. ABSOLUTELY A WASTE OF MONEY!!!! I would buy Schaums outline "Probability, random variables, and random processes."

This is a fantastic book. It is very well written and is a pleasure to read. The problems at the end of each chapter are extensive and help get a very good understanding of the material. This was the required text for a quarter based graduate level course on Statistical Inference. We had an excellent teacher who picked problems very well and that perhaps kept us from getting bogged down. Many of the problems are by no means trivial and require time to solve, which is where a great instructor helps. If you are planning to use this book for self-study, then I would recommend perusing the problem sets from classes, based on this book, that are being offered at some institutions, in order to whittle down the problems to an illustrative subset, before delving into others. Hope this helps.

This is a fantastic book. It is very well written and is a pleasure to read. The problems at the end of each chapter are extensive and help get a very good understanding of the material. This was the required text for a quarter based graduate level course on Statistical Inference. We had an excellent teacher who picked problems very well and that perhaps kept us from getting bogged down. Many of the problems are by no means trivial and require time to solve, which is where a great instructor helps. If you are planning to use this book for self-study, then I would recommend perusing the problem sets from classes, based on this book, that are being offered at some institutions, in order to whittle down the problems to an illustrative subset, before delving into others. Hope this helps.

As the authors of the book "Statistical Inference", we did not participate in the production of the study guide "Outlines and Highlights for Statistical Inference by Casella and Berger". We do not endorse its use, and have always thought that the best way to master this material is to solve problems, not memorize definitions.

George Casella
Roger L. Berger

This book is absolute misery! I would like to echo another review that basically stated if you have to take a class with this book, just drop it now and save yourself the grief. Truer words were never spoken! The Preface states that the prerequisite is 1 year of calculus. That is an outrageous lie! Maybe if you took calculus at Princeton or MIT, you will have a fighting chance. Otherwise you better have the sophistication of writing and understanding proofs that are on par with a real analysis background, and you will definitely need a firm grasp of all the major combinatorial identities and proof techniques before you even attempt to read it, let alone destroy your GPA with it! There is a solution manual floating around the internet, and that too is worthless. Most of the proof techniques used in that rotten book end up as handwaving, and if you have a well trained professor, you will get crushed trying to use some of those techniques. Many of the answers in the solutions manual are just wrong as my professor has PROVEN to us on a number of occasions. The bottom line is dont believe anyone who tells you that 1 year of calculus is enough to read and understand this book. It simply does not apply to most of us, and Casella and Berger should be ashamed of themselves for trying to pass this off as a first year graduate textbook for anyone other than a pure mathematician.

This is the second edition of an excellent book. Casella and Berger put together a text that many faculty began choosing for the first graduate ciurse in mathematical statistics. This second edition is improved over the first and puts more emphasis on the algorithms than the asymptotics. It covers modern topics like resampling and is verywell presented.

When I was a graduate dtudent we used Ferguson and Cox and Hinkley and we also used Lehmann's book for hypothesis testing. This book starts with basic probability and goes on to cover all the bases. It has everything one needs in a modern text on mathematical statistics. I have seen it referenced very often in statistics articles that I had to get a copy for myself in spite of the high price.

I find this book very difficult to read. There are no set margins, and the font set is the same for an example, definition or for a Theory. Trying to find what you are looking for is very time consuming. additionally, the examples are predominantly proofs (which are good), but there are few for applied problems, and the explanations are not very thourough. I would recommend Sheldon Ross Introduction to Probability since it covers the same material, is readable with formatting, and has numerous examples. For an even simpler book to understand, choose Ross, Probability a First Course.

I studies parts of this book years ago, during my grad school days. I found it clear, interesting and well organized. Some reviewers have complained of the low weight given to Bayesian statistics. This is true, this textbook is mostly for folks who want to learn about a frequentist approach. With this caveat, I think it's a very nice introduction to statistics for someone like me who uses statistics within the boundaries of basic applied econometrics. There are typos, but I believe you can find an errata online, which you should be able to locate easily with a google search.

Second year Ph.D. student at Iowa State University.

Covers soft non-measure-theoretic probability theory and statistical theory.
Not extremely rigorous. Appropriate for undergraduates and first-year Master's students. Not appropriate for Ph.D. level courses.

I fear that I may be reiterating what the other reviewers have already said, but I'll put in my two cents anyway. I used Hogg/McKean/Craig's "classic" "Introduction to Mathematical Statistics" for my undergraduate theory class and this one for my Master's level class. I must say that this one was a little bit clearer but omits important topics more often. It's a decent text, but it has its flaws.

First off, I'll talk about the exercises. There is a good amount of variety in problem difficulty ranging from hilariously trivial to taxing, but never too taxing. If you are teaching this class to a mixture of undergraduates and entry-level graduates, you shouldn't have too much trouble coming up with a sizeable list of problems appropriate for one group or the other. However, it will take some work to determine which problems are the difficult ones. Some of the problems that look the easiest are the hardest, which is fine, but they are not arranged or noted in any way so that you can tell which are the hard ones. The trivial ones always come first, but then the exercises jump back and forth between medium difficulty problems and hard problems. Also, I sometimes questioned the problem quality. The problems help the student master the skills, but they don't always come off as relevant in any other way. It's nice when a theory text provides just that--theory, but then let's students see the applications of the theory in the problem set. There is some of this, especially in the early sections on combinatorics (though they were rather contrived), but there should have been more. Another concern that I had is not the book's fault. Since this is a rather popular text, solutions to over half of the problems can be found online. This makes it difficult for the instructor to curb cheating. However, it could be seen as a good thing in one sense, since students like myself often work on non-assigned problems and it's nice to have the solutions readily available.

As far as examples and explanations of theories go, the book is a mixed bag. It seems to do well in the early chapters (probability theory), but it doesn't take extra care in the later, more difficult chapters. I had the hardest time with the Hypothesis Testing chapter. The examples for some of the concepts seemed too slim (usually one per theorem) and the ones presented didn't do a very good job at facilitating understanding. This continued to be a problem in much of the latter half of the book. As far as the proofs go, they are not poorly written, but they often emphasis algebra and formulae over understanding.

Regarding content, the book is a little bit too narrow in its focus. Bayesian statistics is touched on, but it is essentially a text on the theory behind classical statistics. I am of the opinion that classical statistics should be given more weight in an introductory theory class, but I also think that Bayesian statistics deserves more attention than it receives here. Also, it would have been nice to see more information on topics such as non-parametric statistics (virtually absent) and incomplete data. Additionally, it covered quite a bit about general hypothesis testing, but it didn't cover very many commonly used tests. I think that coverage of these tests is important in such a class so that students can see why these tests are used and to know just how important the assumptions behind the tests are. Another omission was that of real world applications (though they aren't entirely absent). I know it's a theory book, but that doesn't mean that applications should be avoided to this degree. Although I wasn't happy about all of these omissions, I can say that what was covered was organized fairly well. Overall, the topics were presented in a logical progression.

One final note: typos and errors. They aren't abundant, but there were more than I would have liked to have seen. There's about as many as most texts on this topic, so it's not a game-breaker.

Second year Ph.D. student at Iowa State University.

I fear that I may be reiterating what the other reviewers have already said, but I'll put in my two cents anyway. I used Hogg/McKean/Craig's "classic" "Introduction to Mathematical Statistics" for my undergraduate theory class and this one for my Master's level class. I must say that this one was a little bit clearer but omits important topics more often. It's a decent text, but it has its flaws.

First off, I'll talk about the exercises. There is a good amount of variety in problem difficulty ranging from hilariously trivial to taxing, but never too taxing. If you are teaching this class to a mixture of undergraduates and entry-level graduates, you shouldn't have too much trouble coming up with a sizeable list of problems appropriate for one group or the other. However, it will take some work to determine which problems are the difficult ones. Some of the problems that look the easiest are the hardest, which is fine, but they are not arranged or noted in any way so that you can tell which are the hard ones. The trivial ones always come first, but then the exercises jump back and forth between medium difficulty problems and hard problems. Also, I sometimes questioned the problem quality. The problems help the student master the skills, but they don't always come off as relevant in any other way. It's nice when a theory text provides just that--theory, but then let's students see the applications of the theory in the problem set. There is some of this, especially in the early sections on combinatorics (though they were rather contrived), but there should have been more. Another concern that I had is not the book's fault. Since this is a rather popular text, solutions to over half of the problems can be found online. This makes it difficult for the instructor to curb cheating. However, it could be seen as a good thing in one sense, since students like myself often work on non-assigned problems and it's nice to have the solutions readily available.

As far as examples and explanations of theories go, the book is a mixed bag. It seems to do well in the early chapters, but it doesn't take extra care in the later, more difficult chapters. I had the hardest time with the Hypothesis Testing chapter. The examples for some of the concepts seemed too slim (usually one per theorem) and the ones presented didn't do a very good job at facilitating understanding. This continued to be a problem in much of the latter half of the book. As far as the proofs go, they are not poorly written, but they often emphasis algebra and formulae over understanding.

Regarding content, the book is a little bit too narrow in its focus. Bayesian statistics is touched on, but it is essentially a text on the theory behind classical statistics. I am of the opinion that classical statistics should be given more weight in an introductory theory class, but I also think that Bayesian statistics deserves more attention than it receives here. Also, it would have been nice to see more information on topics such as non-parametric statistics (virtually absent) and incomplete data. Additionally, it covered quite a bit about general hypothesis testing, but it didn't cover very many commonly used tests. I think that coverage of these tests is important in such a class so that students can see why these tests are used and to know just how important the assumptions behind the tests are. Another omission was that of real world applications (though they aren't entirely absent). I know it's a theory book, but that doesn't mean that applications should be avoided to this degree. Although I wasn't happy about all of these omissions, I can say that what was covered was organized fairly well. Overall, the topics were presented in a logical progression.

One final note: typos and errors. They aren't abundant, but there were more than I would have liked to have seen. There's about as many as most texts on this topic, so it's not a game-breaker.

Second year Ph.D. student at Iowa State University.

I fear that I may be reiterating what the other reviewers have already said, but I'll put in my two cents anyway. I used Hogg/McKean/Craig's "classic" "Introduction to Mathematical Statistics" for my undergraduate theory class and this one for my Master's level class. I must say that this one was a little bit clearer but omits important topics more often. It's a decent text, but it has its flaws.

First off, I'll talk about the exercises. There is a good amount of variety in problem difficulty ranging from hilariously trivial to taxing, but never too taxing. If you are teaching this class to a mixture of undergraduates and entry-level graduates, you shouldn't have too much trouble coming up with a sizeable list of problems appropriate for one group or the other. However, it will take some work to determine which problems are the difficult ones. Some of the problems that look the easiest are the hardest, which is fine, but they are not arranged or noted in any way so that you can tell which are the hard ones. The trivial ones always come first, but then the exercises jump back and forth between medium difficulty problems and hard problems. Also, I sometimes questioned the problem quality. The problems help the student master the skills, but they don't always come off as relevant in any other way. It's nice when a theory text provides just that--theory, but then let's students see the applications of the theory in the problem set. There is some of this, especially in the early sections on combinatorics (though they were rather contrived), but there should have been more. Another concern that I had is not the book's fault. Since this is a rather popular text, solutions to over half of the problems can be found online. This makes it difficult for the instructor to curb cheating. However, it could be seen as a good thing in one sense, since students like myself often work on non-assigned problems and it's nice to have the solutions readily available.

As far as examples and explanations of theories go, the book is a mixed bag. It seems to do well in the early chapters, but it doesn't take extra care in the later, more difficult chapters. I had the hardest time with the Hypothesis Testing chapter. The examples for some of the concepts seemed too slim (usually one per theorem) and the ones presented didn't do a very good job at facilitating understanding. This continued to be a problem in much of the latter half of the book. As far as the proofs go, they are not poorly written, but they often emphasis algebra and formulae over understanding.

Regarding content, the book is a little bit too narrow in its focus. Bayesian statistics is touched on, but it is essentially a text on the theory behind classical statistics. I am of the opinion that classical statistics should be given more weight in an introductory theory class, but I also think that Bayesian statistics deserves more attention than it receives here. Also, it would have been nice to see more information on topics such as non-parametric statistics (virtually absent) and incomplete data. Additionally, it covered quite a bit about general hypothesis testing, but it didn't cover very many commonly used tests. I think that coverage of these tests is important in such a class so that students can see why these tests are used and to know just how important the assumptions behind the tests are. Another omission was that of real world applications. I know it's a theory book, but that doesn't mean that applications should be avoided to this degree. Although I wasn't happy about all of these omissions, I can say that what was covered was organized fairly well. Overall, the topics were presented in a logical progression.

One final note: typos and errors. They aren't abundant, but there were more than I would have liked to have seen. There's about as many as most texts on this topic, so it's not a game-breaker.

I thought there were sample tests in the booklet (85 pages). Not true.
One needs to pay more to get the tests.

Although not particularly advanced, this book is quite specialized and in my opinion, too narrowly focused for a book at this level. It is not a comprehensive introduction to statistical inference. Also, it often focuses on the "what" and the "how" while ignoring the "why".

The book's strengths are self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The mathematical aspects of this book are clean and thorough, and the omissions of certain difficult proofs enhance rather than detract from the book's quality. But as one progresses further in this text, there are many shortcomings. The order in which topics are presented doesn't always seem natural to me.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; not acknowledging other paradigms. This book is mis-named: "Statistical Inference" encompasses much more than what this book covers. The Bayesian paradigm is one area (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material. This book is really about applications of elementary probability theory to frequentist statistics; it is not a general introduction to statistical inference.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and the material on distributions in chapter 3 doesn't probe very far into the particular reasons why certain distributions arise in certain situations. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises helpful. But people interested in the ideas behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations, and as other reviewers have pointed out, the authors do not do a good job of creating a gradient of problems of different difficulty levels. Many of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results. A few of the problems in advanced chapters require truly tedious and lengthy calculations that, in my opinion, are a total waste of a students' time.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or, preferably, by another book that does so. This book will advance a students' understanding of certain topics but it will do little to help the students connect that knowledge with applications or other related theoretical areas. Instructors should be cautious when assigning exercises from this book--there are many excellent exercises but the level of difficulty (as well as the amount students can learn from a given exercise) is highly inconsistent. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text. Another book that is a better alternative is "All of Statistics" by Larry Wasserman; his book is less thorough, but more balanced in terms of perspective, and more focused on helping the reader to learn and understand the underlying ideas.

This is a book that focuses on the "what" and the "how" while ignoring the "why".

The book's strengths are self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The mathematical aspects of this book are clean and thorough, and the omissions of certain difficult proofs enhance rather than detract from the book's quality. But as one progresses further in this text, there are many shortcomings. The order in which topics are presented doesn't always seem natural to me.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; not acknowledging other paradigms. This book is mis-named: "Statistical Inference" encompasses much more than what this book covers. The Bayesian paradigm is one area (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material. This book is really about applications of elementary probability theory to frequentist statistics; it is not a general introduction to statistical inference.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and the material on distributions in chapter 3 doesn't probe very far into the particular reasons why certain distributions arise in certain situations. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises helpful. But people interested in the ideas behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations, and as other reviewers have pointed out, the authors do not do a good job of creating a gradient of problems of different difficulty levels. Many of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results. A few of the problems in advanced chapters require truly tedious and lengthy calculations that, in my opinion, are a total waste of a students' time.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or by another book that does so. This book will advance a students' understanding of certain topics but it will do little to help the students connect that knowledge with applications or other related theoretical areas. Instructors should be cautious when assigning exercises from this book--there are many excellent exercises but the level of difficulty (as well as the amount students can learn from a given exercise) is highly inconsistent. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text. Another book that is a better alternative is "All of Statistics" by Larry Wasserman; his book is less thorough, but more balanced in terms of perspective, and more focused on helping the reader to learn and understand the underlying ideas.

My 3-star rating should be interpreted as 4 or 5 stars for some material and 1 or 2 stars for others. Overall this is a book that focuses on the "what" and the "how" while ignoring the "why".

This book's strengths are self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The mathematical aspects of this book are clean and thorough. Although certain difficult topics or proofs are omitted, I think these omissions enhance rather than detract from the text. As one progresses further in this book, however, the book becomes more lacking. The order in which topics are presented doesn't always seem natural to me.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; while I have no problem with this in and of itself, I have a huge problem with the way the book does not acknowledge other paradigms, and I also think that the book is mis-named, as "Statistical Inference" encompasses much more than what this book covers. The Bayesian approach is one approach (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and some of the remarks made about distributions in chapter 3 are misleading in that they don't probe very far into the particular reasons why certain distributions arise in certain situations: they give the reader the false impression that modeling is much more haphazard and less systematic than it actually is. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises useful and helpful. But people such as myself who are interested in ideas and concepts behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations. A number of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results. A few of the problems in advanced chapters require truly tedious and lengthy calculations that, in my opinion, are a total waste of a students' time.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or by another book that does so. Instructors should be cautious when assigning exercises from this book--there are many excellent exercises but the level of difficulty (as well as the amount students can learn from a given exercise) is highly inconsistent. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text. Another book that is a good alternative is "All of Statistics" by Larry Wasserman; his book is less thorough but more balanced in terms of perspective, and most of the material omitted is of the more tedious nature, detracting little from the stream of ideas.

My 3-star rating should be interpreted as 4 or 5 stars for some material and 1 or 2 stars for others. Overall this is a book that focuses on the "what" and the "how" while ignoring the "why".

The good things about this book are mostly self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The order in which topics are presented doesn't always seem natural to me. As one progresses further in this book, getting into the statistics part, the book becomes more lacking, although coverage of certain topics remains good throughout. The mathematical aspects of this book are clean and thorough. Although certain difficult topics or proofs are omitted, I think these omissions enhance rather than detract from the text.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; while I have no problem with this in and of itself, I have a huge problem with the way the book does not acknowledge other paradigms. The Bayesian approach is one approach (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and some of the remarks made about distributions in chapter 3 are misleading in that they don't probe very far into the particular reasons why certain distributions arise in certain situations: they give the reader the false impression that modeling is much more haphazard and less systematic than it actually is. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises useful and helpful. But people such as myself who are interested in ideas and concepts behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations. A number of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results. A few of the problems in advanced chapters require truly tedious and lengthy calculations that, in my opinion, are a total waste of a students' time.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or by another book that does so. Instructors should be cautious when assigning exercises from this book--there are many excellent exercises but the level of difficulty (as well as the amount students can learn from a given exercise) is highly inconsistent. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text.

My 3-star rating should be interpreted as 4 or 5 stars for some material and 1 or 2 stars for others. Overall this is a book that focuses on the "what" and the "how" while ignoring the "why".

The good things about this book are mostly self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The order in which topics are presented doesn't always seem natural to me. As one progresses further in this book, getting into the statistics part, the book becomes more lacking, although coverage of certain topics remains good throughout. The mathematical aspects of this book are clean and thorough. Although certain difficult topics or proofs are omitted, I think these omissions enhance rather than detract from the text.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; while I have no problem with this in and of itself, I have a huge problem with the way the book does not acknowledge other paradigms. The Bayesian approach is one approach (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and some of the remarks made about distributions in chapter 3 are misleading in that they don't probe very far into the particular reasons why certain distributions arise in certain situations: they give the reader the false impression that modeling is much more haphazard and less systematic than it actually is. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises useful and helpful. But people such as myself who are interested in ideas and concepts behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations. A number of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results. A few of the problems in advanced chapters require truly tedious and lengthy calculations that, in my opinion, are a total waste of a students' time.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or by another book that does so. Instructors should be cautious when assigning exercises from this book--there are many excellent exercises but the level of difficulty (as well as the amount students can learn from a given exercise) is highly inconsistent. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text.

My 3-star rating should be interpreted as 4 or 5 stars for some material and 1 or 2 stars for others. Overall this is a book that focuses on the "what" and the "how" while ignoring the "why".

The good things about this book are mostly self-evident. The exposition of probability theory is excellent, and presented with an eye towards its use in statistics. The order in which topics are presented doesn't always seem natural to me. As one progresses further in this book, getting into the statistics part, the book becomes more lacking, although coverage of certain topics remains good throughout. The mathematical aspects of this book are clean and thorough. Although certain difficult topics or proofs are omitted, I think these omissions enhance rather than detract from the text.

My main criticism of this book is that it presents a narrow view of what statistics is. The book is written from one particular perspective within the frequentist approach; while I have no problem with this in and of itself, I have a huge problem with the way the book does not acknowledge other paradigms. The Bayesian approach is one approach (among many) that is hardly mentioned, and the book doesn't point the reader in directions to cover such material.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and some of the remarks made about distributions in chapter 3 are misleading in that they don't probe very far into the particular reasons why certain distributions arise in certain situations: they give the reader the false impression that modeling is much more haphazard and less systematic than it actually is. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who find manipulations of equations and formulas natural will find the proofs natural and the exercises useful and helpful. But people such as myself who are interested in ideas and concepts behind the equations will find this book lacking. The proofs are clean and easy to follow but many give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge is technical rather than deep--most exercises require a clever or lucky manipulation, and occasionally drawn-out calculations. A number of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results.

I understand why people use this text as a textbook, but in my opinion it needs to be supplemented by something else, either by teacher who focuses on the "why" and the deeper meaning, or by another book that does so. In many ways, I think this book is supplemented or complemented by the text by A.H. Welsh, a book whose weak points are more than covered by this Casella & Berger text.

My 2-star rating should be interpreted as 4 stars for probability theory and 1 star for everything else: this book's treatment of probability is good, but just about everything else is lacking.

The good things about this book are self-evident. The exposition of probability theory is clear, and presented with an eye towards its use in statistics. I find the first chapter to be excellent. The next 4 chapters are usable, although the order in which topics are presented doesn't seem natural to me. As one progresses further in this book (getting into the statistics part), this book becomes more lacking.

My main criticism of this book is that it presents a narrow view of what statistics is, adopting particular perspective within the frequentist approach, and not acknowledging other paradigms. The Bayesian approach is hardly mentioned, and the book provides no tools that would be useful for making inferences about causal relationships, which in my opinion is one of the most important aspects of statistics.

My second criticism of this book is that it is divorced from applications; there is almost no data presented in the text or problems. Discussion of modeling is almost completely absent, and some of the remarks made about distributions in chapter 3 make me wonder if the authors really understand modeling. This remark leads into my next criticism: the book emphasizes symbolic manipulations and ignores the deeper meaning of the mathematics. I think that an understanding of the meaning is critical if one is to find useful applications of the material.

This book is clearly more suited to certain learning styles than others. People who like manipulations of equations and formulas will find the proofs and discussions in this book natural, and the exercises useful and helpful. But people such as myself who are interested in ideas and concepts behind the equations will find this book sorely lacking. The proofs are clean and easy to follow but give little insight into the meaning of the theorems. While the motivated reader can find meaning (sometimes with considerable effort), this book's approach isn't particularly pedagogical. The exercises are numerous and challenging, but the challenge isn't particularly deep--most exercises require a clever or lucky manipulation, and occasionally tedious calculation, and a number of the problems in advanced chapters can be solved without really understanding the implications and meaning of the results.

Bottom line--this book is overpriced and overused, and there are few reasons to use it as a course textbook. I understand that this book serves some people well, but I think it also turns a number of students off to the subject of statistics, and in my opinion, this is a terrible shame. A lot of graduate students using this book simply copy and memorize solutions from the solution manual; while I would never stoop to such a level, I can't blame them for their actions, since honestly I think it is a waste of time to try to learn mathematical statistics from this book.

The book consists of two parts: probability (the first 250 pages) and statistics. The first part is extremely well written; however, the second part (I read page 427 totally so far) is not satisfying. The theorm derivations have missing steps, and not easy to follow. Moreover, it has ERRORS (which are not listed in the errata available in the authors' website). For example, Definition 8.3.16 of monotone likelihood ratio is wrong (page 891): it can only be non-decreasing (cannot be non-increasing). With the wrong definition, no way to approve Thm 8.3.17. I want to ask the author: how did you write down that proof by referring the wrong definition? Another example: Line 5 of example 8.3.19. You cannot draw the conclusion by using the analysis in Example 8.3.18. Instead, you have to use the analysis in Thm 8.3.17! Third example, the definition of power function is not accruate. The definition of power should be independant of H0 or H1. (In fact, the author did a poor job in give the insight of power function. Without such an insight, no way to solution example 8.3.19). Forth example, the second 8.3.4 on p-values is poorly written. The author does not bother to point out that p-values is the smallest level at which we can reject null hypothesis with given samples. Instead, the author's definition on p-values based on an formula whose meaning is very hard to understand! Do you know how many hours I have to spend to figure out these?

Last words to the author who wrote the Hypothesis chapter: pls learn writing from your co-author and then rewrite your chapters!

Very good intro to grad level stats - the problem is that it does not use any real analysis so it is limited if you want to study probability theory at the level of Borovkov or Billingsley. The problems can be tough so a good calculus background is assumed.

Very good intro to grad level stats - does not use any real analysis.

The is one great textbook and is as good as Cormen's introduction to algorithms. It does not require advanced math. I was a biology major and did not learn much Calculus at all. I had to use it in a graduate statistics class. Fortunately we used this book. It is very easy to follow. It gives very good examples and explains them well but not wordy. The exercises are excellent. This book is definitely not an applied statistics book. But it really helps you to understand applied statistics. It is absolutely not just another dry math book. I also want to say that this book is for newcomers. Neither me nor many of my classmates had statistical training before we took the course. When instructors were not clear about something, we always went back to this book and always found an answer.

The is one great textbook and is as good as Cormen's introduction to algorithms. It does not require advanced math. I was a biology major and did not learn much Calculus at all. I had to use it in a graduate statistics class. Fortunately we used this book. It is very easy to follow. It gives very good examples and explains them well but not wordy. The exercises are excellent. This book is definitely not an applied statistics book. But it really helps you to understand applied statistics. It is absolutely not just another dry math book. I also want to say that this book is for newcomers. Neither me nor many of my classmates had statistical training before we took the course. When instructors were not clear about something, we always went back to this book and always found an answer.

This book stinks, if you have to take a course with this book might as well drop out and save yourself thie frustration. The book just has random variables of random variables, and functions of functions. It's ridiculous.

The book will give you one or two examples of each kind of problem. It will then cut you lose like you are a Phd in Mathematics.

The book never provides algorithms to solve any of their problems. This book is written for Casella and Berger's peers.

There has to be an easier way.

Do you remember taking Calculus and doing integrals. How all the class time was spent doing integral problems with trick steps and pretty answers. It won't teach you how to do problems outside of the classroom.

This book stinks, if you have to take a course with this book might as well drop out and save yourself thie frustration. The book just has random variables of random variables, and functions of functions. It's ridiculous.

The book will give you one or two examples of each kind of problem. It will then cut you lose like you are a Phd in Mathematics.

The book never provides algorithms to solve any of their problems. This book is written for Casella and Berger's peers.

There has to be an easier way.

Do you remember taking Calculus and doing integrals. How all the class time was spent doing integral problems with trick steps and pretty answers. It won't teach you how to do problems outside of the classroom.

[1] It is a very very good textbook of frequentist statistics, well self-organized.
[2] The mathematics is precise and clear.
[3] Anyone who is interested in the classical statistics may need such an excellent reference at hand.
[4] If you decide to buy it, you'd better to check the website http://www.campusi.com/, where sometime you can find a surprise.

This book was the recommended companion to my math stat's required textbook. In almost every case where I didn't understand the explanation given in lecture or in the main textbook, I could understand this book's explanation. I cannot vouch for the entire textbook, but I would not have understood MLE without it. The one star missing is because of the book's tendency to mention earlier sections of the book, which was frustrating since I was using it as a reference. Incidentally, I used this edition, but I didn't pay even close to the price here, so definitely comparison shop.

Overall, this book is a solid introduction to mathematical statistics. Exposition is clear and it fully motivates all concepts. I really only have one complaint: this book omits a few topics. A relatively minor example is the absence of the cumulant generating function. More disturbingly is that it does not have a full discussion of the multi-normal distribution (possibly to avoid some non-trivial linear algebra?). However, being that the book is otherwise quite complete and these topics can be found elsewhere these are rather annoyances than fatal flaws.

This book, is not for newcomers to statistics. It often assumes a well versed backround in probability and statistics (and I suppose a decent background in calculus). There is often little explanation for examples and theorems. Often the exercises and examples require the solution to previous exercises. This is extremely frustrating and often discouraging. Many times I would find myself being refered to an example in a previous or future chapter whose solution refers to a problem that needs to worked out. I have an undergraduate degree in math and am by no means a genius, but compared to many well written math texts, the clarity and conciseness leaves much to be desired. The exercises do not go from easier to more difficult but from difficult to difficult. Often the concept that is trying to be illustrated could be done in a much simpler problem.

That all said, the book is fairly well written given the aforementioned weaknesses. My professors seem to like it as do a couple of PhD students.

I use this book for my graduate program too. This is a very good theory book. But I really don't like its problem sets because the most of problems are too complicate. Authors seem to want readers to practice their calculus skill not the full theory understanding. I believe that authors can use other type questions to let readers master their understanding not master their calculus abilty( this is the basic requirement of this book) since this ability belongs to math but statistics.

Another problem for this book, authors do not offer any answers for odd number questions. How can reader practice the exercises without any answers?( I just mean answers not full solutions). If you want to but this book for youself please never try to do the exercises because you never know that you work on the correct direction or not!!!!! Since you won't get any answers.

I found myself wanting to learn statistics and spent many hours browsing the stat books at the Stanford book store - and this book had it all. Some of the proofs are relegated to exercises and this is both fun and maddening! If you have a basic math background - a physicist or engineer equivalent - you will have no problems understanding the book. It's expensive - but you will have months (if not years!) of fun with it. There are many typographical errors in the book but many of them are found in the "errata" at the end. Now, if some one came up with a solution manual for this...

If you have basic training in calculus, you'll love this well written and easy-to-follow book. The book is almost good for self-study. It provides a good introduction to theoretical statistics with good examples.
Compare to many badly written mathematics books by famous mathematicians that gave me terrible experiences, I strongly recommend this book. As I was reading this book, I constantly recalled the hard time I experienced when I used Royden's "Real Analysis" or M. Artin's "Algebra". These two books are classical math textbooks that are appraised by many mathematicians. But according to my knowledge, many students extremely hate these two textbooks simply because these two books are hard to follow unless you read other textbooks. In my eyes, these "bad" textbooks are good only for those who have already mastered the contents (for exmaple, professors who have been teaching this subject for their entire lives). As for me, after I completely understood the topics, I found these two books are quite useful as reference books. But still I believe these two books are not good for entry-level students if they know little about the subjects in the books. As contrary, Casella-Berger's book is very good for entry-level students. Good knowledge in calculus is sufficient for you to easily follow this the topics. Moreover, the content of this book is not simple, it contains almost all of modern statistics.( many poor calculus books are written in such a way that in order to please the students, the author intentionally omitted some important subjects and/or reduced the level of the contents. By doing so, the author became famous and the book went to best-selling, and the students, without any working, are happy to wrongly believe that they know everything while they don't). "Statistical Inference" is good only because it is carefully written. Casella-Berger are not only outstanding researchers, they are also good educators, They know students, they know at what point students would encounter difficulty and at this point, the readers will find an appropriate example to help them out. After reading many bad mathematics textbooks, I believe that mathematician are trying to make our lives more miserable, and this is one of the reasons I lost my interests in mathematics, though I am always good at math. While reading "Statistical Inference", I fell in love with statistics, I'm convinced that statisticians are trying to make our lives better. As I was going through "Statistical Inference", I was also reading Richard Durrett's "Probability: theory and examples", a widely used typical textbook in probability for first year PhD student in statistics. Compare to majority entry-level PhD students in statistics, I have much stronger back ground in mathematics (Lebesgue Measure, Integration and Differentiation), yet I experienced the same hard time as I did in some other math classes. My blame can only go to the bad written textbook, I have to read other textbook to understand the topics, and this is absolutely not good for a not-stupid and hard working student. I am always curious that among all the textbooks available, why mathematicians prefer the textbooks that will give students more hard time. For the same topic, using different explanation, students will have different feelings, why can't the professor pick up the more friendly written books for the sake of student's easy understanding and their continuing interests in the area?

My belief was strengthened after completing the reading of Casella-Berger's "Statistical Inference" and R. Durrett's "Probability", that one must keep away from mathematicians as far as possible since your life will be tough if you are close to them. And as for myself, I won't do research in probability since the book "Probability" gave me the impression that more mathematicians are involved in the area of probability theory. I'll go with Casella Berger, concentrate on the filed of statistical inference since scientists in this particular field are trying to make our lives better and easier.

If you indeed want to learn statistics while having no strong specific back ground, I strongly recommend Casella Berger's "Statistical Inference"!

If you've read a lot of reviews pertaining to texts often used in difficult courses such as physics, grad level math & stats, etc, then you know that invariably a student victimizes a book during the semester. As a student and an instructor, I can safely say that the grade often correlates with the opinion of the book, usually the opinion of the book follows the student's perception of his or her grade in the class. This book is used for some difficult classes, but I can assure you, without being too specific, that it is well written. This material is difficult. I'm not a stats wizard, but I do like the subject area. I will say this: having been a graduate student at the University of Florida, any of the texts authored by the stats faculty there are excellent (ie: Agresti, Mendenhall, Khuri, Casella, and others). It is an outstanding faculty and I have had lectures from all of those professors. Reading their texts is just as clear as listening to them during office hours. My main point is that this is a very good text book. If you want it as a reference, get it. If you want it to supplement another text for your stats class, get it. Just make sure that you have a professor equally as knowledgeable about stats as the author, otherwise, it may be difficult to get help with difficult sections. I suspect the student that wrote from San Diego does not have an instructor that either follows this text closely, or adequately understands the material (I hope it is not the latter). Get this book and keep it around, you will reference before, during, and many years after your studies are through.