Office hours: Mon. 11-12 A.M., Weds. 12-1 P.M.
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. Large sample results will also be presented.
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. The course text is
Lehmann, E.L. (1986). Testing Statistical Hypotheses. Wiley,New York.
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.
Ferguson, T.S. Introduction to Mathematical Statistics, a Decision Theoretic Approach.
Lehmann, E.L. (1983). Theory of Point Estimation. Wiley,New York.
Serfling, R. J. (1980). Approximation Theorems of Mathematical Statistics, Wiley, New York.