Cornell Math - MATH 774, Fall 2000

MATH 774 — Fall 2000
Asymptotic Statistics

The course will provide an introduction to asymptotic statistical decision theory and to empirical stochastic processes. Topics include the notion of experiment, reduction by sufficiency, equivalence classes, the Le Cam delta distance, local asymptotic normality and minimaxity, optimal rates of convergence and the Pinsker bound, and Gaussian approximation of nonparametric experiments. On the empirical process side, we discuss coupling theorems, some probability metrics, entropy conditions, functional limit theorems, and Hungarian constructions. The concept of Hellinger process in martingale theory may also be covered, and its applications to the statistics of diffusion processes.

Suggested prerequisites are measure theoretic probability, including stochastic processes, and basic mathematical statistics.