Homoscedasticity tests for both low and high-dimensional fixed design regressions

Abstract

This paper is to prove the asymptotic normality of a statistic for detecting the existence of heteroscedasticity for linear regression models without assuming randomness of covariates when the sample size $n$ tends to infinity and the number of covariates $p$ is either fixed or tends to infinity. Moreover our approach indicates that its asymptotic normality holds even without homoscedasticity.

19 pages

References in corpus (2)

• Invariance principles for homogeneous sums: Universality of Gaussian Wiener chaos
• Invariance principles for homogeneous sums of free random variables

Cited by in corpus (1)

• Robust Inference Under Heteroskedasticity via the Hadamard Estimator