嘉宾简介  Introduction

Runze Li is the Eberly Family Chair in Statistics, the Pennsyvlania State University. His research includes variable selection for high-dimensional data, feature screening for ultrahigh dimensional data, nonparametric and semiparametric regression modeling, and statistical applications to social behavioral science, neural science and engineering. He is a fellow of Institute of Mathematical Statistics, a fellow of American Statistical Association and a fellow of American Association for the Advancement of Science. He received various honors and awards including The United Nations' World Meteorological Organization Gerbier-Mumm International Award for 2012 and ICSA Distinguished Achievement Award in 2017. He served as editor of Annals of Statistics from 2013 to 2015.

报告简介  Course Content

We introduce a novel approach for high-dimensional regression with theoretical guarantees. The new procedure overcomes the challenge of tuning parameter selection of Lasso and possesses several appealing properties. It uses an easily simulated tuning parameter that 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 maintaining high efficiency for normal random errors. Computationally, it can be efficiently solved via linear programming. Theoretically, under weak conditions on 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. Our results make useful contributions to mending the gap between the practice and theory of Lasso and its variants. We also prove that further improvement in efficiency can be achieved by a second-stage enhancement with some light tuning. Our simulation results demonstrate that the proposed methods often outperform cross-validated Lasso in various settings.

讲座海报Poster