Introduction to Mathematical Statistics

Paul Hoel taught statistics at UCLA for many years. This book was one of the best introductions to mathematical statistics for a first year graduate course. It was used as a text for that purpose at UCLA and many other statistics departments across the country. Several editions of the book were published to keep it up to date. Currently it is a little dated and there are many advances particularly in the area of resampling methods and other computer-intensive statistical procedures that are not covered. I think it is somewhat comparable to the combination of Erich Lehmann's books on hypothesis testing and the theory of estimation.

I used the fourth edition in a college course and found it to be well written and very understandable (the fourth edition was pre-calculator and had math tables in the back). The book assumed only an elementary calculus background and so was not rigorous in proving every theorem introduced, but was pretty good in showing the derivation of commonly used results and formulas. I particularly liked the problem sets which were a mix of theoretical and applied exercises (with answers to the odd numbers), and NOT a long list of statements to be proven. The emphasis was on theory, but statistical theory developed from attempts to solve real life problems and this book recognized that and considered applications of that theory throughout.