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A Distributionally Robust Estimator that Dominates the Empirical Average

Nikolas P. Koumpis
Dionysis Kalogerias
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\chi^{2}-robust mean squared error problem in closed form.

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