论文标题
鲁棒风险最小化的渐近正态性
Asymptotic normality of robust risk minimizers
论文作者
论文摘要
本文研究了算法的渐近特性，这些特性可以看作是经典经验风险最小化的强大类似物。这些策略是基于均值代表均值代表通常的经验平均值，例如（版本）平均值估计器的中位数。到目前为止，众所周知，产生估计器的多余风险通常以最佳的速率在较弱的假设下以比其``经典''对应物要求的假设差。然而，对于估计量本身的渐近性质，最大可能性估计量的鲁棒类似物是否渐近效率，知之甚少。我们朝着回答这些问题迈出了一步，并表明，对于广泛的参数问题，将风险适当定义的强大代表的最小化器最小化融合了以相同的速率以相同速率的真实风险的最小化，并且通常具有相同的渐近差异，与估算器相同，通过使平常的经验风险最小化来获得估计器。
This paper investigates asymptotic properties of algorithms that can be viewed as robust analogues of the classical empirical risk minimization. These strategies are based on replacing the usual empirical average by a robust proxy of the mean, such as the (version of) the median of means estimator. It is well known by now that the excess risk of resulting estimators often converges to zero at optimal rates under much weaker assumptions than those required by their ``classical'' counterparts. However, less is known about the asymptotic properties of the estimators themselves, for instance, whether robust analogues of the maximum likelihood estimators are asymptotically efficient. We make a step towards answering these questions and show that for a wide class of parametric problems, minimizers of the appropriately defined robust proxy of the risk converge to the minimizers of the true risk at the same rate, and often have the same asymptotic variance, as the estimators obtained by minimizing the usual empirical risk.
