Robust Mean Estimation for Optimization: The Impact of Heavy Tails
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918455661297664 |
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| author | van Parys, Bart P. G. Zwart, Bert |
| author_facet | van Parys, Bart P. G. Zwart, Bert |
| contents | We consider the problem of constructing a least conservative estimator of the expected value $μ$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $μ$ 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 $μ$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21421 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Robust Mean Estimation for Optimization: The Impact of Heavy Tails van Parys, Bart P. G. Zwart, Bert Optimization and Control Probability Statistics Theory 60F10, 62G35, 90C17 We consider the problem of constructing a least conservative estimator of the expected value $μ$ of a non-negative heavy-tailed random variable. We require that the probability of overestimating the expected value $μ$ 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 $μ$ 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. |
| title | Robust Mean Estimation for Optimization: The Impact of Heavy Tails |
| topic | Optimization and Control Probability Statistics Theory 60F10, 62G35, 90C17 |
| url | https://arxiv.org/abs/2503.21421 |