Robust statistics is a fairly mature field that dates back to the early 1960s, with many foundational concepts having been developed in the ensuing decades. However, the field has drawn a new surge of attention in the past decade, largely due to a desire to recast robust statistical principles in the context of high-dimensional statistics. In this article, we begin by reviewing some of the central ideas in classical robust statistics. We then discuss the need for new theory in high dimensions, using recent work in high-dimensional M-estimation as an illustrative example. Next, we highlight a variety of interesting recent topics that have drawn a flurry of research activity from both statisticians and theoretical computer scientists, demonstrating the need for further research in robust estimation that embraces new estimation and contamination settings, as well as a greater emphasis on computational tractability in high dimensions.

中文翻译：

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现代稳健统计的理论回顾


稳健统计是一个相当成熟的领域，可以追溯到 1960 年代初，在接下来的几十年里已经开发了许多基本概念。然而，该领域在过去十年中引起了新的关注，主要是由于希望在高维统计的背景下重塑稳健的统计原则。在本文中，我们首先回顾了经典稳健统计中的一些中心思想。然后，我们以最近在高维 M 估计方面的工作作为说明性例子，讨论了高维新理论的必要性。接下来，我们重点介绍了最近各种有趣的主题，这些主题吸引了统计学家和理论计算机科学家的一系列研究活动，表明需要进一步研究稳健估计，包括新的估计和污染设置，以及更加强调高维的计算可处理性。