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Statistics Department Seminar presents "On the minimax optimality of maximum likelihood in the non-Donsker regime"

On the minimax optimality of maximum likelihood in the non-Donsker regime
Tuesday, January 12, 2021 - 4:30pm
Gil Kur (MIT)
Abstract / Description: 

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 may 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 ≥ 5.

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

The Statistics Seminars for Winter Quarter will be held online via Zoom at 4:30pm on Tuesdays. Please note that these events will be locked by the Host after ten minutes, so latecomers will not be able to join the Meeting. Subscribe to Statistics distribution list to receive Meeting IDs and passwords via email.