Seminar Details

Seminar Details


Oct 24

3:30 pm

Consistency and Rates of Convergence for Maximum Likelihood Estimators via Empirical Process Theory

Jon A. Wellner


University of Washington - Department of Statistics

Empirical process methods play an important role in the study of maximum likelihood and minimum contrast estimators in non-parametric and semi-parametric models. In this talk I will begin with a short review of modern Glivenko-Cantelli theorems and inequalities for empirical processes. I will then survey some of the basic inequalities for proving consistency of MLE’s, illustrated by several examples from current or recent research projects. Finally, I will review the results concerning (global) rates of convergence of MLE’s due to Wong and Shen, Birg´e and Massart, and van de Geer (1996). Although MLE’s can be rate sub-optimal when the entropy is of sufficiently “high entropic dimension”, MLE’s continue to perform extremely well relative to competitors for non-parametric problems with “low entropic dimension”, including a number of interesting mixture models and problems with interval censoring.

The talk will conclude with several challenges and open problems.