Course: STAT 30100
Title: Mathematical Statistics I
Instructor: Chao Gao
Class Schedule: Sec 1: TR 9:30 AM–10:50 PM in TBA
Description: This course is part of a two-quarter sequence on the theory of statistics. Topics are grouped into four parts: sufficiency and exponential family, statistical decision theory, estimation under constraint, and asymptotic theory. Specific topics include sufficiency, exponential family, minimal sufficiency, completeness, Rao-Blackwell theorem, decision theory, Bayes estimator, minimaxity, admissibility, James-Stein estimator, empirical Bayes, nonparametric density estimation, Gaussian sequence model, blockwise James-Stein, Neyman-Pearson lemma, Le Cam’s two point method, UMVUE, Stein’s unbiased risk estimate, location family, equivariance, Pitman estimator, scale family, location-scale family, MLE consistency, score, Fisher information, MLE asymptotic normality, local asymptotic normality, differentiable under quadratic mean, Bernstein-von Mises theorem, Cramer-Rao lower bound, Hodges’ estimator, superefficiency, almost everywhere convolution theorem, and local asymptotic minimaxity.