Product Description

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.

Product Details

• Amazon Sales Rank: #49526 in Books
• Published on: 2001-06-18
• Original language: English
• Number of items: 1
• Binding: Hardcover
• 688 pages

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."

Customer Reviews

A good book with a few weak points..
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.

Very complete advanced introduction to statistics
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.

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 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.