Math 6263

Spring 2001

Professor Spruill

Meets 12:05-12:55 MWF in 240 Skiles

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 multiparameter 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. Selected topics from sequential testing, optimality of the SPRT, and large sample theory will also be presented.

Grading

Your grade for the course will be determined by your performance on two midterm exams, a final exam, and problem sets. Each will count one fourth. Problems will be assigned during the semester.

The course is classical in content, but connections to decision-theoretic and Bayesian statistics are established. See the summary of some results from MA6262 for information relating to these areas.

There is no course text apart from our notes . The following references are useful and will be placed on reserve. Some collateral information on invariance is available.

• Lehmann, E.L. (1986). Testing Statistical Hypotheses. Wiley,New York.
• 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.