With random regressors, least squares inference is robust to correlated errors with unknown correlation structure.

ABSTRACT: Linear regression is arguably the most widely used statistical method. With fixed regressors and correlated errors, the conventional wisdom is to modify the variance-covariance estimator to accommodate the known correlation structure of the errors. We depart from existing literature by showing that with random regressors, linear regression inference is robust to correlated errors with unknown correlation structure. The existing theoretical analyses for linear regression are no longer valid because even the asymptotic normality of the least squares coefficients breaks down in this regime. We first prove the asymptotic normality of the t statistics by establishing their Berry-Esseen bounds based on a novel probabilistic analysis of self-normalized statistics. We then study the local power of

SUBMITTER: Zhang Z 

PROVIDER: S-EPMC12320931 | biostudies-literature | 2025

REPOSITORIES: biostudies-literature