American Statistical Association
New York City
Metropolitan Area Chapter

Levin Lecture Series: Spring 2019 Colloquium Seminars
Department of Biostatistics
Mailman School of Public Health
Columbia University



A TUNING-FREE APPROACH TO HIGH-DIMENSIONAL REGRESSION

by

Lan Wang
Professor
School of Statistics
University of Minnesota

Host: Dr. Min Qian


Abstract

We introduce a new tuning-free approach for high-dimensional regression with theoretical guarantee. The new procedure possesses several appealing properties simultaneously. Computationally, it can be efficiently solved via linear programming with an easily simulated tuning parameter, which automatically adapts to both the unknown random error distribution and the correlation structure of the design matrix. It is robust with substantial efficiency gain for heavy-tailed random errors while maintains high efficiency for normal random errors. It enjoys an essential scale-equivariance property that permits coherent interpretation when the response variable undergoes a scale transformation, a desirable property possessed by the classical least squares estimator but lost by Lasso and its variants. Under weak conditions for the random error distribution, we establish a finite-sample error bound with a near-oracle rate for the new estimator with the simulated tuning parameter.

This is joint work with Bo Peng, Jelena Bradic, Runze Li and Yunan Wu.


Date: Thursday, March 28, 2019
Time: 11:45 A.M. - 12:45 P.M.
Location: Mailman School of Public Health
Department of Biostatistics
722 West 168th Street
AR Building
8th Floor Auditorium
New York, New York

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