Nonparametric Screening Under Conditional Strictly Convex Loss for Ultrahigh Dimensional Sparse Data

• Activity Number: 580 - Statistical and Computational Challenges in Nonparametric Learning
• Type: Topic Contributed
• Date/Time: Thursday, August 6, 2020 : 3:00 PM to 4:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Xu Han*
• Companies: Temple University
• Keywords: ultrahigh dimensional variable selection; sure screening property; goodness-of-fit nonparametric screening; conditional strictly convex loss

Abstract

Sure screening technique has been considered as a powerful tool to handle the ultrahigh dimensional variable selection problems, where the dimensionality p and the sample size n can satisfy the NP dimensionality (Fan & Lv 2008). The current paper aims to simultaneously tackle the “universality" and “effectiveness" of sure screening procedures. For the “universality", we develop a general and unified framework for nonparametric screening methods from a loss function perspective. Consider a loss function to measure the divergence of the response variable and the underlying nonparametric function of covariates. We newly propose a class of loss functions called conditional strictly convex loss. The sure screening property will be established within this class of loss functions. For the “effectiveness", we focus on a goodness of fit nonparametric screening (Goffins) method under conditional strictly convex loss. The superior performance of our proposed method has been further demonstrated by extensive simulation studies and some real scientific data example.