Catoni proposed a robust M-estimator and gave the deviation inequality for one fixed test function. The present paper is devoted to the uniform concentration inequality for a family of test functions. As an application, we consider empirical risk minimization for heavy-tailed losses.
翻译:Catoni 提出了一个稳健的 M- 估测器, 并给出了一个固定测试功能的偏差不平等。 本文专门论述测试功能大家庭的统一集中不平等问题。 作为应用,我们考虑将重尾损失的经验风险降到最低。