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 $\chi^{2}-$robust mean squared error problem in closed form.

翻译：我们利用风险规避与分布鲁棒优化之间的对偶关系，设计了一种分布鲁棒估计器，该估计器对所有具有负超额峰度的概率分布均严格优于经验均值。上述估计器以闭式解的形式解决了$\chi^{2}-$鲁棒均方误差问题。