2025/03/27 by Bart P. G. van Parys, Bart P. G. Van Parys, Bert Zwart +2 · 1 voice
Decision Sciences · Engineering · Mathematics · #60F10 #62G35 #90C17 #Advanced Statistical Process Monitoring #Control Systems and Identification #FOS: Mathematics #Fault Detection and Control Systems #Optimization and Control (math.OC) #Probability (math.PR) #Statistics Theory (math.ST) #math.OC #math.PR #math.ST
paper · pdf · doi:10.48550/arxiv.2503.21421
openalex publication_date 2025/03/27 · arxiv published 2025/03/27 · openalex created_date 2025/10/11 · arxiv updated 2026/04/20 · openalex updated_date 2026/07/28
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.