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Revisiting Huber’s M-Estimation: A Tuning-Free Approach

Presented by: 
Chao Zheng
Tuesday 30th January 2018 - 11:00 to 12:00
INI Seminar Room 2
We introduce a novel scheme to choose the scale or robustification parameter in Huber’s method for mean estimation and linear regression in both low and high dimensional settings, which is tuning-free. For robustly estimating the mean of a univariate distribution, we first consider the adaptive Huber estimator with the robustification parameter calibrated via the censored equation approach. Our theoretical results provide finite sample guarantees for both the estimation and calibration parts. To further reduce the computational complexity, we next develop an alternating M-estimation procedure, which simultaneously estimates the mean and variance in a sequential manner. This idea can be naturally extended to regression problems in both low and high dimensions. We provide simple and fast algorithms to implement this procedure under various scenarios and study the numerical performance through simulations.

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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons