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Robust and sparse estimators for linear regression models

Banff International Research Station for Mathematical Innovation and Discovery

Penalized regression estimators are a popular tool for the analysis of sparse and high-dimensional data sets. However, most of the proposals of penalized regression estimators are defined using unbounded loss functions, and therefore are very sensitive to the presence of outlying observations, especially high leverage outliers. Thus, robust estimators for sparse and high-dimensional linear regression models are in need. In this talk, we in- troduce Bridge and adaptive Bridge versions of MM-estimators: q -penalized MM-estimators of regression and MM-estimators with an adaptive t penalty. We discuss their asymptotic properties and outline an algorithm to calculate them for the special case of q = t = 1. The advantages of our proposed estimators are demonstrated through a simulation study and the analysis of a real high- dimensional data set.

Mathematics; Statistics

video/mp4

Author affiliation: University of Buenos Aires - CONICET

2016-05-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58168

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/