Nonparametric Independence Screening via Favored Smoothing Bandwidth

TL;DR

This paper introduces a nonparametric regression approach for ultrahigh-dimensional data, utilizing a favored smoothing bandwidth for efficient variable screening and an iterative method for accurate covariate and function recovery.

Contribution

It presents a novel screening method based on favored smoothing bandwidth, with proven model selection consistency and demonstrated effectiveness through simulations and real data.

Findings

The screening method is computationally efficient.

It achieves consistent variable selection.

It performs well in practical applications.

Abstract

We propose a flexible nonparametric regression method for ultrahigh-dimensional data. As a first step, we propose a fast screening method based on the favored smoothing bandwidth of the marginal local constant regression. Then, an iterative procedure is developed to recover both the important covariates and the regression function. Theoretically, we prove that the favored smoothing bandwidth based screening possesses the model selection consistency property. Simulation studies as well as real data analysis show the competitive performance of the new procedure.