Customer Reviews

Statistical Inference

5 star:		(19)
4 star:		(8)
3 star:		(10)
2 star:		(2)
1 star:		(2)

 

 

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 course 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 student 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 and I decided that I had to get a copy for myself in spite of the high price. i think this should be one of the preferred texts for the first year PhD course in mathematical statistics. It certainly requires a full year of calculus as would any good math stat book but the level is even higher than that and that also should be expected by the students.

Typically first year PhD students in statistics would take this course concurrently with a course in advanced probability that includes measure theory. So the measure theory knowledge gained by the student in the probability course will and should be needed for the latter chapters of this math stat course.

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, and as such I think it is misnamed; "Statistical Inference" encompasses much more than what this book covers. This book is really about "classical" statistics and it does not acknowledge or integrate more modern ways of looking at things, even when they could be presented at an elementary level. The Bayesian paradigm is hardly mentioned, non-parametric approaches are hardly mentioned, and decision theory is ignored. As such, I don't see how it offers any improvement over older texts, such as Hogg and Craig.

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 mechanically (even though they are not easy) 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 other books that do 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. As a more advanced and more philosophical text, and to cover decision theory and Bayesian methods in more depth, I would recommend "Statistical Decision Theory and Bayesian Analysis" by J.O. Berger.

Like many statisticans, I used this book in my Grad program. Needless to say, I've read the book from cover to cover many, many times. As theory goes, I think this book is excellent. However, I believe the major weakness of this books lies in it's examples and problem sets. I believe that (even for advanced texts) the problem sets should have a difficulty gradient to them (starts out with easier problems and ends with the real brain twisting tough problems), and this books does seem to do that to a degree, but it does not do it very well. In addition to this, there are many problem sets in the book where it is very easy to get lost in the math and completely miss the important statistical point/lesson that should be illustrated. Many of the most difficult problems of the book have very little to do with statistics and more to do with mathematics.

The authors also have the annoying habit of refering to the results of previous problems/excercises. Therefore, in order to do some exercises/examples, you must go back and work one or two of the exercises from one of the previous chapters. The book would have been a lot more helpful if the author would provide the solutions for exercises that he intends to build upon.

IMHO the best introduction to Probability Theory and Inferential Statistics. Because it doesn't say "Mathematical Statistics" in the title I ignored it for years and iterated between several other good texts. But Casella & Berger is more accurate, more up-to-date, and/or more fun to read. It strikes a better balance among topics and among schools of thought. It is furthermore exceptionally lucid and original, and very carefully edited. The organisation of the text is perfectly coherent, but this doesn't make it easy to skip difficult parts or concepts. The use of the book is also somewhat constrained by the author's effort at using nonstandard and challenging examples and problems (euphemistically called exercises). In practice I have to provide standard exercises to (econometrics) students as additional material. I am slightly uneasy with the unequal treatment of some items, many being emphasized as numbered propositions whereas others are just mentioned in the text. I similarly regret the cursory treatment of asymptotic distributions and asymptotic efficiency (for the purposes of econometrics). I do not like the exposition of Analysis Of Variance, but on the other hand I marvel at the stimulating treatment of linear regression in the last chapter.

Quibbles apart, Casella & Berger is a demanding but most rewarding and stimulating introduction to (so-called) mathematical statistics, and in particular it is exceptionally dependable and witty. Beginning students may require some complementary material in the form of standard exercises and worked-out examples.

Casella and Berger have written an excellent book on mathematical statistics, perfect for the first year graduate student. This book is different from other books (i.e. Lehmann) in that it has a thorough introduction to basic probability theory, for those who might need the review. The theorems in this book are more thorough and complete than in some other books (i.e. Bickel and Doksum). Unfortunately, this book is priced rather highly for those with a casual interest in statistics. However, if price is not an issue, I would strongly recommend this book. I refer to it often.

If you have basic training in calculus, you'll love this well written, easy-to-follow book. It provides a complete list of theories along with rigorous proofs and comprehensive examples, by which it is almost good for self-study.

Comparing with many badly written mathematical books by famous names that gave me terrible experiences, I strongly recommend this book. As I was enjoying reading of this book, my memory constantly went back to the difficult time I had experienced when I tried so hard on Royden's "Real Analysis" or M. Artin's "Algebra". These two are classical math textbooks that are appraised by the majority of mathematicians. But from my observation, quite a few students hate these two books to some extreme, because they are so hard to follow unless you read other textbooks. In my opinion, these "bad" textbooks are good only for those who have already mastered the contents (for example, professors who have been teaching this subject for their entire lives). After completely understood the topics, I found these two books are quite useful as reference books. But still I do not think these two books are good to begin with if the reader knows 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 the topics. Moreover, the content of this book is not simple; it contains almost all aspects of univariate 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. 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 excellent educators. They know students, they know at what point students would encounter what difficulty and at this point, you definitely will find an appropriate example to help you out. The sharp contrasts between "Statistical Inference" and many "bad" textbooks in mathematics convince me that mathematicians are trying to make our lives more miserable (and this is one of the reasons I lost my interests in mathematics, though I have been good at math) while statisticians are trying to make our lives easier.

At the same time of 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. Compared with majority entry-level PhDs in statistics, my background in mathematics (Lebesgue Measure, Integration and Differentiation) is no weaker, 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 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 approaches, 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 inferences since scientists in this particular field are trying to make our lives better and easier.

In conclusion, if you need to learn statistics while having no specific back ground, I strongly recommend Casella Berger's "Statistical Inference"..

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.

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.

I used this book as a first year graduate student in statistics. My undergrad degree was not in statistics, I think those that had an undergraduate degree in statistics enjoyed this book more. My main problem with it was that after this book I knew HOW to do a problem, or WHAT a theorem was, I could PROVE and DERIVE things, but I was really lacking in UNDERSTANDING. I had to spend many hours asking questions of my professors about what all the things I was doing actually meant, or why I was doing them. As I learn more about statistics, this book becomes better because I can put it all in context. Just last semester, I probably would have said I didn't like this book at all, but now I'd say it's okay. Just note it's shortcomings.

Also, I have the paperback "international" version. The international version has VERY cheap paper and a lame binding. If you are going to spend as many hours as I did with this book, you should just suck it up and buy the expensive hardcover version. The paper for the paperback is practically see-through and makes it tougher to read.

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.