Dimension reduction-based significance testing in nonparametric regression

TL;DR

This paper introduces a new dimension reduction-based adaptive test for assessing the significance of covariates in nonparametric regression, effectively mitigating the curse of dimensionality and improving test performance.

Contribution

It proposes a novel adaptive-to-model significance test that behaves like a local smoothing test with reduced dimensionality, enhancing power and significance level control in high-dimensional settings.

Findings

The new test effectively detects local alternatives with fewer covariates.

Simulation studies show improved power and significance level maintenance.

Real data analysis confirms practical effectiveness.

Abstract

A dimension reduction-based adaptive-to-model test is proposed for significance of a subset of covariates in the context of a nonparametric regression model. Unlike existing local smoothing significance tests, the new test behaves like a local smoothing test as if the number of covariates were just that under the null hypothesis and it can detect local alternatives distinct from the null at the rate that is only related to the number of covariates under the null hypothesis. Thus, the curse of dimensionality is largely alleviated when nonparametric estimation is inevitably required. In the cases where there are many insignificant covariates, the improvement of the new test is very significant over existing local smoothing tests on the significance level maintenance and power enhancement. Simulation studies and a real data analysis are conducted to examine the finite sample performance of the proposed test.