SILO



The weekly SILO Seminar Series is made possible through the generous support of the 3M Company and its Advanced Technology Group

3M

with additional support from the Analytics Group of the Northwestern Mutual Life Insurance Company

Northwestern Mutual

Fitting high-dimensional linear models by M-estimation: some surprising asymptotic phenomena

Derek Bean, Prof.

Date and Time: Oct 15, 2014 (12:30 PM)
Location: Orchard room (3280) at the Wisconsin Institute for Discovery Building

Abstract:

This talk reviews some recent work on (unpenalized) linear re- gression M-estimators in high-dimensions. Extending the seminal work of Peter Huber, Steve Portnoy and others to the setting where n, the number of ob- servations, is large and comparable to p, the number of predictors, we obtain updated results for the asymptotic statistical behavior of the estimates. Some surprising phenomena are revealed, including:
1. The maximum likelihood estimate is generally suboptimal in terms of asymptotic variance;
2. The optimal objective function amongst all M-estimates can be computed, and it depends on certain aspects of the statistical model as well as the limit of the ratio p/n.
I will also present some extensions to penalized regression M-estimates. This talk covers joint work with Noureddine El Karoui, Peter Bickel, Chinghway Lim, and Bin Yu.