Topics
Decision theoretic and classical treatments of testing statistical hypotheses including, univariate testing in simple and composite cases, exponential families, generalized Neyman-Pearson lemma and application to UMPU single parameter tests, locally best tests, testing in multivariate Koopman Darmois families, similarity and completeness, application to UMPU tests, including the one and two sample t-tests, group invariance and UMPI tests including the general linear model, sequential testing, optimality of the SPRT.
Your grade for the course will be determined by your performance on a midterm exam, a final exam, and problem sets. Each will count one third. Problems will be assigned during the quarter from the course text,
Introduction to Mathematical Statistics, a Decision Theoretic Approach, by T.S. Ferguson.
and from other sources.
The following problems are from Ferguson. page problems 204 1,2,3,5,7 297 2,3 213 1,2,4,7 233 3,5,6 247 1,3,4,7 272 2,3,8 256 3,4 325 1,2,3,4,6,7 369 3,6 383 1,3,7,11
Some important references are as follows: Berger, J.W.(1985). Statistical Decision Theory and Bayesian Analysis. Springer-Verlag,New York. DeGroot, M.(1970). Optimal Statistical Decisions, McGraw-Hill, New York. Lehmann, E.L. (1983). Theory of Point Estimation. Wiley,New York. Lehmann, E.L. (1986). Testing Statistical Hypotheses. Wiley,New York. Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.