Jon A Wellner
Limit theorems, asymptotic methods, asymptotic efficiency and efficiency bounds for estimation, maximum likelihood estimation, Bayes methods, asymptotics via derivatives of functionals, sample-based estimates of variability: (bootstrap and jackknife); robustness; estimation for dependent data, nonparametric estimation and testing. Prerequisite: STAT 513; either MATH 426 or MATH 576. Offered: A.
Use of limit theory in statistics: central limit theorems, modes of convergence, continuous mapping theorems, asymptotic linearity of statistics. Asymptotic normality of sample quantiles and some basic large sample theory for empirical distribution functions. Cramer-Rao efficiency bounds in the presence of nuisance parameters, and the geometry of efficienty estimation. Large sample theory of maximum likelihood estimtors and the related test statistics: Wald, Rao (or score), and likelihood ratio statistics.
Student learning goals
General method of instruction
Lecture with weekly homework sets.
Statistics 512-513 or equivalent. Math 424-425-426.
Class assignments and grading