Variance Estimation with Dependence and Heterogeneous Means

TL;DR

This paper introduces a conservative variance estimator that remains valid under dependence and heterogeneity in means, addressing biases in standard estimators for complex data structures.

Contribution

It proposes a robust variance estimator for sums of dependent, heterogeneously meaned random vectors, ensuring accurate inference in complex dependence settings.

Findings

The estimator is asymptotically valid under two-way cluster dependence.

Standard estimators underestimate variance under heterogeneity and dependence.

The proposed method improves test accuracy in dependent data scenarios.

Abstract

This paper considers the problem of estimating the variance of a sum of a triangular array of random vectors with heterogeneous means. When random vectors exhibit two-way cluster dependence or weak dependence, standard variance estimators designed under homogeneous means can underestimate the true variance, which results in subsequent tests being oversized. To restore validity, this paper proposes a simple conservative variance estimator robust to heterogeneous means and shows its asymptotic validity.