Testing Heteroskedasticity in High-Dimensional Linear Regression

TL;DR

This paper introduces a new heteroskedasticity test for high-dimensional linear regression models using Lasso residuals, demonstrating its theoretical validity and practical effectiveness through simulations and real data applications.

Contribution

It develops a novel heteroskedasticity testing method suitable for high-dimensional settings where the number of covariates exceeds the sample size.

Findings

Test statistic is asymptotically normal under null hypothesis.

The method achieves accurate size and power in simulations.

Effective in real economic data analysis.

Abstract

We propose a new testing procedure of heteroskedasticity in high-dimensional linear regression, where the number of covariates can be larger than the sample size. Our testing procedure is based on residuals of the Lasso. We demonstrate that our test statistic has asymptotic normality under the null hypothesis of homoskedasticity. Simulation results show that the proposed testing procedure obtains accurate empirical sizes and powers. We also present results of real economic data applications.