- Hardcover: 660 pages
- Publisher: Duxbury Press; 2nd edition (June 18, 2001)
- Language: English
- ISBN-10: 0534243126
- ISBN-13: 978-0534243128
- Product Dimensions: 6.5 x 1.2 x 9.3 inches
- Shipping Weight: 2.1 pounds (View shipping rates and policies)
- Average Customer Review: 3.6 out of 5 stars See all reviews (72 customer reviews)
- Amazon Best Sellers Rank: #215,274 in Books (See Top 100 in Books)
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Statistical Inference 2nd Edition
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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."
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Top Customer Reviews
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.
Unless you already have an understanding of statistical theory or are required to have this text for your course, I cannot recommend it. While it is theoretical and states in the introduction that only two semesters of calculus is sufficient for using the text, in practice things are quite another matter. There are a few positives. I appreciate that the text offers a breadth of topics not included in many others, and that is a positive aspect of the book. While unhelpful, I enjoy the Sherlock Holmes quotes. The selected font is nice. The tables outline distributions and their attributes are very helpful.
As for the shortcomings, I find, as a student new to the field on a theoretical level, there are many.
First is the structure of the book, itself: I have never had a math book competing with a novel for size. That is to say, the text is compact and the book small, with implications that you are reading dense paragraphs about both math and theory. This makes the material hard to follow and easy to get lost in.
Second, while there are several examples given in the text, none are ever worked out in their entirety, not even as an appendix or supplement. Therefore, the book assumes quite a lot of the reader/student/novice and simply tells you that "simple calculus" or "steps from chapter X" are useful in completing a problem. This is a curious tactic, as those with experience teaching math will know that the best way to learn is to see examples worked out over and over again, with no steps omitted. If a student were to submit for grading the work put forth in the book, points would be lost due to the lack of proper hashing out of the steps. And the only way to learn said steps are by seeing them...in one's text.
Third, the book has a maddening habit of referring the reader to exercises as a means of explanation within the chapter. Another odd choice in teaching mechanisms, considering that if the student knew the concept, he/she would not be reading the book and would not require the practice in the first place.
Fourth, the exercises are not organized in any logical fashion. That is to say, when one references a math text, problems sets begin simply so to reinforce the concept and build confidence with the student. Then, more challenging problems are introduced to test the knowledge and skill of the student. This text jumps right to the testing phase of questions without the skill-building set...frustrating for students trying to work out challenging concepts in ways that are generally not intuitive.
Fifth, the examples within the text are not written in a fashion that one would experience them in an exam or even in the chapter exercises of this very book! That is to say, no clear question is given at the start of the "example." Rather, steps are covered without you knowing the true starting point.
Sixth, there are no practice problems within the text. This would be helpful.
Seventh, it is rare that any of the theoretical concepts are provided context so that you have an idea of what the concept is used for in an applied setting, making the content even more difficult to grasp.
Finally, the index is not particularly useful, as it is not very thorough. A student is better off making their own notes with reference pages as they go along, rather than rely on the index, which seems to only cover main topics (oddly enough, already covered in the contents).
In summary, studying this book makes me feel as though the student should know statistical theory before they know statistical theory...or know the subject before they find the book in any way useful. The authors do not seem to have a clear goal of whether this book should be used as a reference or teaching tool...and so have created a tome with a confusing combination of aspects of both. I am regularly consulting several books at once (and searching the Internet and consulting professors) in order to make sense of much of the text, further supporting the fact that while this book has breadth, the depth is sadly lacking.
While the authors allude to the logic of Sherlock Holmes, the hours I spend squeezing sense out of this book rather calls to mind the nonsensicalness of Lewis Carroll's "Alice in Wonderland." Thus, I spend much of my time down the rabbit hole.
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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Already using the book so cant return and exchange right now.
Needed the code too.Read more