Testing Statistical Hypotheses

E.L. Lehmann is Professor of Statistics Emeritus at the University of California, Berkeley. He is a member of the National Academy of Sciences and the American Academy of Arts and Sciences, and the recipient of honorary degrees from the University of Leiden, The Netherlands and the University of Chicago. He is the author of Elements of Large-Sample Theory and (with George Casella) he is also the author of Theory of Point Estimation, Second Edition. Joseph P. Romano is Professor of Statistics at Stanford University. He is a recipient of a Presidential Young Investigator Award and a Fellow of the Institute of Mathematical Statistics. He has coauthored two other books, Subsampling with Dimitris Politis and Michael Wolf, and Counterexamples in Probability and Statistics with Andrew Siegel.

1. The general decision problem; 2. The probability background; 3. Uniformly most powerful tests; 4. Unbiasedness: Theory and first applications; 5. Unbiasedness: Applications to normal distributions; Confidence intervals; 6. Invariance; 7. Linear hypotheses; 8. Multivariate linear hypotheses; 9. The minimax principle; 10. Conditional inference.