Robust Mean Estimation for Optimization: The Impact of Heavy Tails

Bart P. G. van Parys; Bert Zwart

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arXiv · 2503.21421

Robust Mean Estimation for Optimization: The Impact of Heavy Tails

Bart P. G. van Parys·Bert Zwart

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Abstract

We consider the problem of constructing a least conservative estimator of the expected value $\mu$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $\mu$ is kept appropriately small; a natural requirement if its subsequent use in a decision process is anticipated. In this setting, we show it is optimal to estimate $\mu$ by solving a distributionally robust optimization (DRO) problem using the Kullback-Leibler (KL) divergence. We further show that the statistical properties of KL-DRO compare favorably with other estimators based on truncation, variance regularization, or Wasserstein DRO.

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Bart P. G. van Parys, Bert Zwart. 2025-03-27. Robust Mean Estimation for Optimization: The Impact of Heavy Tails. https://arxiv.org/abs/2503.21421

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