Customer Reviews

Testing Statistical Hypotheses (Springer Texts in Statistics)

5 star:		(3)
4 star:		(1)
3 star:		(1)
2 star:		(1)
1 star:		(0)

 

 

This text was commonly used as a graduate text in mathematical statistics in the 1970s when I was a graduate student at Stanford University. It was the best and most detailed text on the theory of hypothesis testing. Over the years it remained so and twenty years after publication, when it was outdated by research advances it was revised by Professor Lehmann. The second edition originally published by Wiley went out of print but has now been reprinted by Springer-Verlag. This is a great book for any statistician to have on his bookshelf, a must have reference!

The 3rd edition has an entirely new set of chapters covering asymptotics. I found this to be a very readable survey, including a good discussion of local asymptotic normality, which is not treated in more elementary texts. There's some overlap between this book and Lehman's Theory of Point Estimation. It's not obvious which should be read first, but both books are very well written with many interesting problems.

Lehmann and Romano, Third Edition, fourth printing, 2008, is a wonderful, beautiful, necessary book for the shelf of every serious statistician, but in a few ways it is not quite right. Some important topics are omitted. At least one important topic is much more important than the book says. At least one statement, while correct, may be read incorrectly by beginners. At least one proof is unreadable.

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, but there exists an exact Monte Carlo test for blocks and treatments which works correctly in the presence of heteroskedasticity. 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 unable to follow the (very short) proof of Theorem 9.1.3. The complexity of the notation is perhaps responsible.

Every professional statistician should have a copy of this book. I lent my copy of the first edition to somebody I can't remember and of course never got it back--no surprise since it is absolutely indispensable. So I purchased this third edition. It's worth it. The book is a classic and Erich Lehmann is a genius.

I found this book hard to read & maneuver around in. Maybe I should've gotten an earlier edition.

This is a textbook for theoretical statistics,which has more content than 2nd edition while the 2nd edition is concise and pointed. If it is not required to have third edition, I would rather buy the 2nd edition.

I received the book after 5 days of purchase. It is pretty new and clean.