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51 of 56 people found the following review helpful
5.0 out of 5 stars good text for first graduate course in statistics
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...
Published on October 15, 2007 by Michael R. Chernick

versus
105 of 112 people found the following review helpful
3.0 out of 5 stars Good, but with many shortcomings. Too specialized, and improperly named
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...
Published on February 25, 2007 by Alexander C. Zorach


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105 of 112 people found the following review helpful
3.0 out of 5 stars Good, but with many shortcomings. Too specialized, and improperly named, February 25, 2007
This review is from: Statistical Inference (Hardcover)
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.
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51 of 56 people found the following review helpful
5.0 out of 5 stars good text for first graduate course in statistics, October 15, 2007
This review is from: Statistical Inference (Hardcover)
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.
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72 of 87 people found the following review helpful
5.0 out of 5 stars Excellent on introduction to univariate statistics, June 16, 2003
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This review is from: Statistical Inference (Hardcover)
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"..
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22 of 25 people found the following review helpful
3.0 out of 5 stars Review by a Grad Student, March 27, 2010
By 
E. Ward (Cambridge, ma USA) - See all my reviews
(REAL NAME)   
This review is from: Statistical Inference (Hardcover)
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.
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14 of 15 people found the following review helpful
3.0 out of 5 stars Respectable, July 9, 2007
By 
Leicester Dedlock (Ames, IA United States) - See all my reviews
This review is from: Statistical Inference (Hardcover)
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.
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18 of 21 people found the following review helpful
5.0 out of 5 stars very good, but it is difficult material for many people, January 21, 2003
By 
todd (GAINESVILLE, FLORIDA United States) - See all my reviews
This review is from: Statistical Inference (Hardcover)
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.
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14 of 16 people found the following review helpful
5.0 out of 5 stars One of the best textbooks, July 14, 2006
This review is from: Statistical Inference (Hardcover)
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.
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16 of 19 people found the following review helpful
5.0 out of 5 stars Great textbook., December 4, 2007
By 
This review is from: Statistical Inference (Hardcover)
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.
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10 of 11 people found the following review helpful
3.0 out of 5 stars Hit or Miss, May 30, 2010
This review is from: Statistical Inference (Hardcover)
Pretty solid textbook overall.

Pros:
1. Thorough introduction to classical statistics. This text hits most of the major topics in frequentist statistics.
2. Clear exposition, at least in the first 7 chapters.
3. Good selection and variety of problems. See below.

Cons:
1. Some important topics are omitted. One that comes to mind is the Multivariate Normal Distribution. A little more Bayesian material would have been nice. Also, some other topics could very well have been omitted which are fairly non standard (ie Union Intersection tests.)
2. Chapters 8-10 are not nearly as strong as the previous chapters. I often had to turn to other sources for additional examples and explanations.
3. Some problems are a complete waste of time. This is my biggest gripe with an otherwise great textbook. Too many problems require drawn out, extremely tedious calculations. Others require leaps of intuition which even seasoned statisticians would not make. My advice is to ask someone who has gone through the problems for recommendations. Or, if a problem is taking a very long time, take a look at the first few lines of the solution - you may save yourself a lot of wasted time.
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9 of 10 people found the following review helpful
4.0 out of 5 stars Very good coverage of calculus-based probability., July 10, 2009
This review is from: Statistical Inference (Hardcover)
This is a very good book to use as a first semester introductory course for Stat PhD. If you know some advanced calculus and a little math stat, you can use the first 5 or 6 chapters to get serious about statistics. Learn all of the standard probability distributions, and derive as many of their properties as you can. The book is straight-forward and will allow one to build a string foundation in the basics by working a large number of problems.

To me, the second half of the book never seemed as strong as the first half of the book. The second half of the book could be used in the second semester, but the instructor would have to supplement the material. I think this is why many programs use this book for only the first semester, and then switch to another book or note packet.
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Statistical Inference
Statistical Inference by George Casella (Hardcover - June 18, 2001)
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