Variance Estimation with Dependence and Heterogeneous Means

Luther Yap

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arXiv · 2603.11497

Variance Estimation with Dependence and Heterogeneous Means

Luther Yap

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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.

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Luther Yap. 2026-03-12. Variance Estimation with Dependence and Heterogeneous Means. https://arxiv.org/abs/2603.11497

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