Open Collections

Robust penalized M-estimators

Banff International Research Station for Mathematical Innovation and Discovery

Data sets where the number of variables p is comparable to or larger than the number of observations n arise frequently nowadays in a large variety of fields. High dimensional statistics has played a key role in the analysis of such data and much progress has been achieved over the last two decades in this domain. Most of the existing procedures are likelihood based and therefore quite sensitive to deviations from the stochastic assumptions. We study robust penalized M-estimators and discuss some of their formal robustness properties. In the context of high dimensional generalized linear models we provide oracle properties for our proposals. We discuss some strategies for the selection of the tuning parameter and extensions to generalized additive models. We illustrate the behavior of our estimators in a simulation study.

Mathematics; Statistics

video/mp4

Author affiliation: University of Geneva

2016-05-20

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/58169

Unreviewed

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