- Series: Springer Texts in Statistics
- Paperback: 800 pages
- Publisher: Springer (November 19, 2010)
- Language: English
- ISBN-10: 1441931783
- ISBN-13: 978-1441931788
- Product Dimensions: 6.1 x 1.8 x 9.2 inches
- Shipping Weight: 2.5 pounds (View shipping rates and policies)
- Customer Reviews: 10 customer ratings
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Testing Statistical Hypotheses (Springer Texts in Statistics) Paperback – November 19, 2010
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From the reviews of the third edition:
"This new edition of the classic and fundamental text on the theory of testing hypotheses is an essential addition to the bookshelf of mathematical statisticians." Short Book Reviews of the International Statistical Institute, December 2005
"What I like much about this book is its illustrative language and the numerous examples that make it easier to understand the complex matter presented. The comprehensible notation and the excellent structure further add to the readability of this book."Biometrics, March 2006
"The third edition of TSH retains much of the same focus as the second edition...The quality of the new material alone justifies the publication of a third edition to a book already well suited. As readers of the earlier editions have come to expect, TSH contains an enormous number of examples, problems, and ideas. The writing and presentation are excellent." Journal of the American Statistical Association, June 2006
"This is the third edition of a famous book which was first published in 1959. The first rigorous exposition to the theory of testing for any student of statistics has been invariably through this masterpiece. … Needless to say, this book continues to be the benchmark in the rigorous treatment of testing of hypothesis. The new chapters on the asymptotic behaviour of most of the popular tests is a true value addition." (Arup Bose, Sankhya, Vol. 67 (4), 2005)
"This is a revised and expanded version of the well-known second edition from 1986 … . The exposition is clear and sufficiently rigorous. … With this edition ‘Testing Statistical Hypothesis’ will undoubtedly continue to be the standard graduate level textbook on statistical testing." (R. Schlittgen, Zentralblatt MATH, Vol. 1076, 2006)
"This monograph under review is the third edition … of Erich L. Lehmann’s classical graduate text on ‘Testing statistical hypotheses’. … the second edition from 1986 has comprehensively been reorganized … . Additional insight into the historical background and recent developments is given … . More than 1,000 original references are provided. … an excellent and demanding treatment of modern statistical test theory. There is no doubt that it remains and will even more be used as a standard monograph … ." (J. Steinebach, Metrika, Vol. 64, 2006)
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Reading through the books after you learn the topic will make you feel the beauty and the idea lies behind the statistics. I remembered when I read the first few sections of chapter 3 over 20 times when I learn this topic. It's hard, but precise, and I don't know if anyone else could explain it any better. So this book deserves your endeavor, not only your passion.
Finally, as other people said, not too much detail, and some topics, are missing. However, to my belief, the topics included represents the history, that's when they actually put statistical testing into great use, and these are the topics that has been thoroughly discussed and studied. So maybe that's why it is a little outdated. But classic is always classic. And undoubtedly the best book to read.
An omission is heteroskedasticity. The usual tests for 2-samples and k-samples are wrong in its presence. The same is true for the usual test for blocks and treatments. However, for all these there do exist tests which are conservative in the presence of heteroskedasticity. For 2-samples and for two treatments there are exact tests. Another omission is Doob's inequality for nonnegative martingales, which connects up some Bayes tests with some frequentist tests.
Simpson's paradox (page 132 bottom) is treated at length in the book, but the treatment does not suffice, and there might not be any treatment which could suffice. The paradox strikes at nearly all of what statisticians do. The book ought to use big bold-face type for the statement of the paradox. Also, the book ought to include an example, not just give a reference.
The account of Monte Carlo tests (page 442) may seem to suggest that Monte Carlo gives only an approximation and that its accuracy depends on how many random numbers are used. The reader is not told that Monte Carlo tests are commonly exact tests for small samples. (And where in the book is the word "exact"?)
On page 353 I am entirely unable to follow the (very short) proof of Theorem 9.1.3. The complexity of the notation is perhaps responsible.