Linear hypothesis testing in high-dimensional heteroscedastics via random integration

TL;DR

This paper introduces a novel random integration method for high-dimensional heteroscedastic linear hypothesis testing, providing asymptotic properties and demonstrating improved power through simulations and real data analysis.

Contribution

It proposes a new random integration approach based on the L2-norm for heteroskedastic GLHT in high dimensions, with asymptotic analysis and practical validation.

Findings

The test approximates the null distribution with a chi-square type mixture.

The proposed method is more powerful than existing tests.

Numerical simulations and real data confirm effectiveness.

Abstract

In this paper, for the problem of heteroskedastic general linear hypothesis testing (GLHT) in high-dimensional settings, we propose a random integration method based on the reference L2-norm to deal with such problems. The asymptotic properties of the test statistic can be obtained under the null hypothesis when the relationship between data dimensions and sample size is not specified. The results show that it is more advisable to approximate the null distribution of the test using the distribution of the chi-square type mixture, and it is shown through some numerical simulations and real data analysis that our proposed test is powerful.