High-dimensional Ordinary Least-squares Projector for Screening Variables
Abstract
Variable selection is a challenging issue in many statistical applications when the number of predictors p far exceeds the number of observations n. In this ultra-high dimensional setting, Fan and Lv (2008) introduced the sure independence screening (SIS) procedure that can significantly reduce the dimensionality while preserving the true model with overwhelming probability, before a refined second stage analysis. However, the aforementioned sure screening property strongly relies on the assumption that the important variables in the model should have large marginal correlations with the response, which rarely holds in reality. Motivated by these concerns, we propose a novel and simple screening technique called the high-dimensional ordinary least-squares projector (HOLP) for high dimensional features. We show that HOLP possesses the sure screening property and gives consistent variable selection without the strong assumption, and has a low computational complexity. Simulation study shows that HOLP performs competitively compared to many other marginal correlation based methods including (iterative) SIS, forward regression and tilting. An application to a mammalian eye disease data illustrates the attractiveness of HOLP. This is joint work with Xiangyu Wang in Duke.
Background
Chenlei Leng joined Warwick as a professor of statistics in 2013. He is interested in developing statistical models for analyzing small and big datasets. He received his bachelor’s degree in mathematics from USTC, China and PhD in statistics from the University of Wisconsin-Madison. He is an elected member of the International Statistical Institute and currently serves as an associate editor of the Journal of the Royal Statistical Society, Series B.
Research Interests
Chenlei’s research interests span the areas of high dimensional data analysis, model selection, semi- and non-parametric statistics, longitudinal data analysis, quantile regression, and applied statistics.