Gil KUR (MIT) – ” On the Minimax Optimality of the Maximum Likelihood in the non-Donsker regime “

November 9, 2:00 pm - 3:15 pm

The Statistical Seminar: Every Monday at 2:00 pm.

Time: 2:00 pm – 3:15 pm
Date: 9th of November 2020
Place: Visio

Gil KUR (MIT)  – ” On the Minimax Optimality of the Maximum Likelihood in the non-Donsker regime

Abstract: The minimax optimality of the Maximum Likelihood Estimator (MLE) is a fundamental question in mathematical statistics. For Donsker classes, it is well-known that the MLE is minimax optimal. However, in the non-Donsker regime, the MLE could be minimax sub-optimal. In this talk, we present new techniques to evaluate the statistical performance of the MLE in the non-Donsker regime. As an application, we demonstrate that the log-concave MLE is optimal in all dimensions. In comparison, for convex regression, the MLE can be suboptimal when \$d \ge 5\$.

This talk is based on joint work with Dagan, Gao, Guntuboyina, Rakhlin and Sen.

Organizers:
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Zoltan SZABO (CMAP)