Nonparametric Independence Screening in Sparse Ultra-High Dimensional Varying Coefficient Models

TL;DR

This paper introduces nonparametric independence screening methods for variable selection in ultra-high dimensional varying-coefficient models, demonstrating their theoretical properties and practical effectiveness through simulations and real data.

Contribution

It proposes novel marginal nonparametric screening techniques with proven sure screening properties for ultra-high dimensional sparse models.

Findings

NIS effectively reduces dimensionality in ultra-high dimensional settings.

Conditional-INIS and Greedy-INIS improve variable selection accuracy.

Methods perform well in simulations and real data applications.

Abstract

The varying-coefficient model is an important nonparametric statistical model that allows us to examine how the effects of covariates vary with exposure variables. When the number of covariates is big, the issue of variable selection arrives. In this paper, we propose and investigate marginal nonparametric screening methods to screen variables in ultra-high dimensional sparse varying-coefficient models. The proposed nonparametric independence screening (NIS) selects variables by ranking a measure of the nonparametric marginal contributions of each covariate given the exposure variable. The sure independent screening property is established under some mild technical conditions when the dimensionality is of nonpolynomial order, and the dimensionality reduction of NIS is quantified. To enhance practical utility and the finite sample performance, two data-driven iterative NIS methods are proposed for selecting thresholding parameters and variables: conditional permutation and greedy methods, resulting in Conditional-INIS and Greedy-INIS. The effectiveness and flexibility of the proposed methods are further illustrated by simulation studies and real data applications.