Heteroscedasticity Testing for Regression Models: A Dimension Reduction-based Model Adaptive

TL;DR

This paper introduces a dimension reduction-based heteroscedasticity test for regression models that adapts to the underlying data structure, improving performance over traditional methods especially in moderate dimensions.

Contribution

It proposes a novel model adaptive test that reduces dimensionality, behaves like a local smoothing test, and has an asymptotically normal distribution under the null hypothesis.

Findings

Test statistic is asymptotically normal under null hypothesis

Finite sample performance is validated through simulations

Real data analysis demonstrates practical effectiveness

Abstract

Heteroscedasticity testing is of importance in regression analysis. Existing local smoothing tests suffer severely from curse of dimensionality even when the number of covariates is moderate because of use of nonparametric estimation. In this paper, a dimension reduction-based model adaptive test is proposed which behaves like a local smoothing test as if the number of covariates were equal to the number of their linear combinations in the mean regression function, in particular, equal to 1 when the mean function contains a single index. The test statistic is asymptotically normal under the null hypothesis such that critical values are easily determined. The finite sample performances of the test are examined by simulations and a real data analysis.