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"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."
--This text refers to an out of print or unavailable edition of this title.
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.
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Most Helpful Customer Reviews
15 of 15 people found the following review helpful
Format:Hardcover
A thorough description of statistical theory from the fundamental premices to the major results. Progress throughout the book is carefully structured, with thought even given to the numbering of theorems and examples so that the reader feels comfortable and progress is easy to follow. There is little digression into other areas of maths, with a little vector notation being as hard as it gets. As a result, the prerequisites are few and the flow is uninterrupted.
Since Amazon don't, at time of writing, have a table of contents for this book, I'll give a brief run down: Simple probability ideas - intersection/union of events, conditional probability and Bayes probability; random variables - general relationships, functions, etc.; families of distributions - normal, gamma, exponential, etc.; random sampling - theorems, implications, expectation/variance, etc.; normal random variables - implications of the particularisation of previous theories; point estimation theory - how to generate an estimator and how to judge performance; hypothesis testing - formulating and evaluating tests; interval estimation - generating confidence intervals for point estimates, relationship to hypothesis testing. There are one or two other chapters, but these are the only ones I've read thoroughly. There's no reason to believe the others aren't as impressive as these, though.
3 of 3 people found the following review helpful
Format:Paperback
Statistical Inference by Casella is without doubt a classic when it comes to statistical theory. Whether you're an undergraduate or postgraduate, if you're covering statistical theory, this is the book for you.
The explanations and definitions are succinct without leaving out any of the important stuff. Additionally, the proofs and multiple examples make understanding so much more concrete.
I had always shied away from this text as many say it's an advanced graduate text and far too hard for what it's worth. Those people couldn't be more wrong! It is a hefty book and quite advanced, and if you majored in statistics, you'd be using it throughout your degree, but nonetheless it's a bible of sorts.
I've replaced all my other statistics texts with this one.
As an aside, if I had to find one fault with this text, it would be that it's chapter on regression is quite weak and doesn't make use of matrices (despite them being used elsewhere). That said, it's still more intuitive than other texts.
The explanations and definitions are succinct without leaving out any of the important stuff. Additionally, the proofs and multiple examples make understanding so much more concrete.
I had always shied away from this text as many say it's an advanced graduate text and far too hard for what it's worth. Those people couldn't be more wrong! It is a hefty book and quite advanced, and if you majored in statistics, you'd be using it throughout your degree, but nonetheless it's a bible of sorts.
I've replaced all my other statistics texts with this one.
As an aside, if I had to find one fault with this text, it would be that it's chapter on regression is quite weak and doesn't make use of matrices (despite them being used elsewhere). That said, it's still more intuitive than other texts.
Format:Paperback|Amazon Verified Purchase
This is probably the "bible" of Statistical inference. However, from a students point of view it is, in my opinion, worth little more than the heat you can get from burning it. This text seems to be written by professors for professors with professors in mind. The book is extremely terse and the author bothers little in helping the student understand the subtleties of the arguments in proofs and examples, many of which are hard to follow, are extremely subtle, terse, and assume you have a very excellent knowledge of what has been written in earlier chapters. So unless you have acquired and encyclopedic knowledge of the earlier parts of the book and the numbering of Theorems and examples you will find yourself looking backwards and forwards to find what example or theorem 1.2.3.4, which you may have studied months ago, said.
The author only grudgingly and occasionally provides the poor reader with hints as to how to get from one step in an agreement to the next. Worse still some of the proofs are not clearly delineated as such and you have to be extremely alert to work out how some of the theorems are arrived at. In some cases the proof is given in un-delineated text before the statement of the proof causing considerable confusion.
The typography is completely unhelpful (the first edition was better) and a dyslexic's nightmare. All of the examples are quite abstract.
The author indulges in the irritating and unhelpful practice of leaving numerous aspects "as an exercise" or as one of the numerous exercises in the book of which there are a large number. A cardinal sin in my opinion. These exercise are also extremely subtle in places. The is an on line solutions manual for the exercises, however, in the style of the book these are extremely terse and hard to follow.
The first half of the book contains a treatment of probability. This contains a superficial treatment of Boreal fields which is completely unsatisfactory and really should have been left out. The second half a treatment of inference proper.
The author seems to have forgotten that the purpose of a text book is to communicate with the reader and help them understand. This book makes the process of understanding statistical inference, which is not easy in the first place, even harder as you have to decode his style and method of presentation. This may well be a bible of Statistical Inference, but, you will have to learn the Statistical equivalent of ancient Greek to understand it.
You may conclude that I do not like this book, and you would be right. The frightening thing is that there appears to be no alternative.
The author only grudgingly and occasionally provides the poor reader with hints as to how to get from one step in an agreement to the next. Worse still some of the proofs are not clearly delineated as such and you have to be extremely alert to work out how some of the theorems are arrived at. In some cases the proof is given in un-delineated text before the statement of the proof causing considerable confusion.
The typography is completely unhelpful (the first edition was better) and a dyslexic's nightmare. All of the examples are quite abstract.
The author indulges in the irritating and unhelpful practice of leaving numerous aspects "as an exercise" or as one of the numerous exercises in the book of which there are a large number. A cardinal sin in my opinion. These exercise are also extremely subtle in places. The is an on line solutions manual for the exercises, however, in the style of the book these are extremely terse and hard to follow.
The first half of the book contains a treatment of probability. This contains a superficial treatment of Boreal fields which is completely unsatisfactory and really should have been left out. The second half a treatment of inference proper.
The author seems to have forgotten that the purpose of a text book is to communicate with the reader and help them understand. This book makes the process of understanding statistical inference, which is not easy in the first place, even harder as you have to decode his style and method of presentation. This may well be a bible of Statistical Inference, but, you will have to learn the Statistical equivalent of ancient Greek to understand it.
You may conclude that I do not like this book, and you would be right. The frightening thing is that there appears to be no alternative.
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Most Recent Customer Reviews
Statistical Inference
A slight North American bias can rapidly be overcome.
This book should only be considered as part of a taught course: do not try to read this on your own!
This book should only be considered as part of a taught course: do not try to read this on your own!
Published 17 months ago by timp
A student point of view
I don't like the book. The explenations are not organized. It goes on and on about a concept with out get to the right point. But it is a complete book. Read more
Published on 18 Mar 2007 by Nasim Babaei
My Text Book/Handbook in Statistical Inference
This is a crucially important text book. I use it frequently for my references in my field. It is my 'classical' text book.
Published on 31 Oct 2003
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