A Distributionally Robust Estimator that Dominates the Empirical Average

2024/02/16 by Nikolas Koumpis, Koumpis, Nikolas, Kalogerias, Dionysis
Agricultural and Biological Sciences · Decision Sciences · Mathematics · #Advanced Statistical Methods and Models #Agricultural risk and resilience #FOS: Mathematics #Risk and Portfolio Optimization #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.2402.10418

openalex publication_date 2024/02/16 · openalex created_date 2024/02/20 · openalex updated_date 2026/07/28

Abstract

We leverage the duality between risk-averse and distributionally robust optimization (DRO) to devise a distributionally robust estimator that strictly outperforms the empirical average for all probability distributions with negative excess kurtosis. The aforesaid estimator solves the χ²-robust mean squared error problem in closed form.

Related

• Distributionally Robust Optimization and Robust Statistics
• Recovering Best Statistical Guarantees via the Empirical\n Divergence-based Distributionally Robust Optimization
• Robust Mean Estimation for Optimization: The Impact of Heavy Tails
• A data-driven approach to beating SAA out-of-sample
• Statistics of Robust Optimization: A Generalized Empirical Likelihood Approach