Statistical Inference [Hardcover]

George Casella (Author), Roger L. Berger (Author)

Book Description

ISBN-10: 0534243126 | ISBN-13: 978-0534243128 | Publication Date: June 18, 2001 | Edition: 2

This book builds theoretical statistics from the first principles of probability theory. Starting from the basics of probability, the authors develop the theory of statistical inference using techniques, definitions, and concepts that are statistical and are natural extensions and consequences of previous concepts. Intended for first-year graduate students, this book can be used for students majoring in statistics who have a solid mathematics background. It can also be used in a way that stresses the more practical uses of statistical theory, being more concerned with understanding basic statistical concepts and deriving reasonable statistical procedures for a variety of situations, and less concerned with formal optimality investigations.

Editorial Reviews

Review

"Statistical Inference is a delightfully modern text on statistical theory and deserves serious consideration from every teacher of a graduate- or advanced undergraduate-level first course in statistical theory. . . Chapters 1-5 provide plenty of interesting examples illustrating either the basic concepts of probability or the basic techniques of finding distribution. . . The book has unique features [throughout Chapters 6-12] for example, I have never seen in any comparable text such extensive discussion of ancillary statistics [Ch. 6], including Basu's theorem, dealing with the independence of complete sufficient statistics and ancillary statistics. Basu's theorem is such a useful tool that it should be available to every graduate student of statistics. . . The derivation of the analysis of variance (ANOVA)F test in Chapter 11 via the union-intersection principle is very nice. . . Chapter 12 contains, in addition to the standard regression model, errors-in-variables models. This topic will be of considerable importance in the years ahead, and the authors should be thanked for giving the reader an introduction to it. . . Another nice feature is the Miscellanea Section at the end of nearly every chapter. This gives the serious student an opportunity to go beyond the basic material of the text and look at some of the more advanced work on the topics, thereby developing a much better feel for the subject."

Product Details

• Hardcover: 660 pages
• Publisher: Duxbury Press; 2 edition (June 18, 2001)
• Language: English
• ISBN-10: 0534243126
• ISBN-13: 978-0534243128
• Product Dimensions: 9.3 x 6.3 x 1.2 inches
• Shipping Weight: 2.1 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (41 customer reviews)
• Amazon Best Sellers Rank: #52,276 in Books (See Top 100 in Books)

Customer Reviews

Most Helpful Customer Reviews

45 of 47 people found the following review helpful:

5.0 out of 5 stars good text for first graduate course in statistics, October 15, 2007

By 

Michael R. Chernick "statman31147" (Holland PA) - See all my reviews
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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.

64 of 69 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

By 

Alexander C. Zorach "Alex Zorach" (Lancaster, PA) - See all my reviews
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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.

120 of 134 people found the following review helpful:

3.0 out of 5 stars A good book with a few weak points.., July 20, 2001

By 

Drew Balazs (Indianola, WA United States) - See all my reviews

This review is from: Statistical Inference (The Wadsworth & Brooks/Cole Statistics/Probability Series) (Hardcover)

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.