BIOS 7204 - Advanced Statistical Theory I

[3 Credits]

Three hours of lecture per week. A mathematical study of the classical theory of statistical inference. Moment generating functions and characteristic functions, distributions of order statistics, exponential family of distributions, models of convergence, the Cramer-Rao inequality, efficiency, best unbiased estimation, completeness, minimal sufficiency, maximum likelihood estimators; monotone likelihood ratio, unbiased and invariant hypothesis tests, generalized likelihood ratio tests, Bayes’ and minimax procedures. Prerequisite: BIOS 6206.