Variance Estimation with Dependence and Heterogeneous Means
arXiv:2603.11497
The paper develops a framework for variance estimation when data exhibit dependence and heterogeneous means, showing that consistent estimation is generally impossible and providing conditions and an optimal eigenvalue‑truncation estimator that is robust to these challenges.
Abstract
This paper develops a framework for variance estimation under dependence and heterogeneous means. This paper shows that consistent estimation of the variance target is impossible in general, and characterizes necessary and sufficient conditions for conservative variance estimation using dual cones. To choose among the valid estimators, this paper formulates three criteria -- minimal correction, pointwise level estimand, and pointwise MSE -- and shows how an eigenvalue truncation solution is optimal under all three criteria. This characterization and solution allow us to assess if existing variance estimators are valid and optimal in their respective settings, and construct the first optimal variance estimator that is simultaneously robust to heterogeneous means and cross-cluster serial correlation.