Nonparametric Independence Screening via the Variance of the Regression Function

• Activity Number: 131
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Won Chul Song*+ and Michael G. Akritas
• Companies: Penn State and Penn State
• Keywords: Sure independence screening ; Ultrahigh dimensionality ; Variable selection ; Nonparametric regression

Abstract

This article develops a procedure for screening variables, in ultrahigh-dimensional settings, based on their predictive significance. This is achieved by ranking the variables according to the variance of their respective marginal regression functions (RV-SIS). This is in sharp contrast with most existing literatures on feature screening, which ranks the variables according to a correlation measure with the response, and hence select variables with no predictive power (e.g., variables that influence aspects of the conditional distribution of the response other than the regression function). The RV-SIS is easy to implement and does not require any model specification for the regression functions (such as linear or other semi-parametric modeling). We show that, under some mild technical conditions, the RV-SIS possesses a sure screening property, which is defined by Fan and Lv (2008). Numerical comparisons suggest that RV-SIS has competitive performance compared to other screening procedures, and outperforms them in many different model settings, including when covariates influence aspects of the conditional distribution of the response other than the regression function.