$M$-functionals of multivariate scatter

IF 11 Q1 STATISTICS & PROBABILITY

Statistics Surveys Pub Date : 2013-12-19 DOI:10.1214/15-SS109

L. Duembgen, Markus Pauly, T. Schweizer

引用次数: 23

Abstract

This survey provides a self-contained account of M-estimation of multivariate scatter. In particular, we present new proofs for existence of the underlying M-functionals and discuss their weak continuity and differentiability. This is done in a rather general framework with matrix-valued random variables. By doing so we reveal a connection between Tyler's (1987) M-functional of scatter and the estimation of proportional covariance matrices. Moreover, this general framework allows us to treat a new class of scatter estimators, based on symmetrizations of arbitrary order. Finally these results are applied to M-estimation of multivariate location and scatter via multivariate t-distributions.

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$M$-多元散射的泛函

这项调查提供了一个独立的多变量散点的m估计的帐户。特别地，我们给出了新的m泛函存在性的证明，并讨论了它们的弱连续性和可微性。这是在具有矩阵值随机变量的相当一般的框架中完成的。通过这样做，我们揭示了泰勒(1987)散点的m泛函和比例协方差矩阵的估计之间的联系。此外，这个一般框架允许我们处理一类新的基于任意阶对称的散射估计。最后，将这些结果应用于多变量位置的m估计，并通过多变量t分布进行分散。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Statistics Surveys STATISTICS & PROBABILITY-

CiteScore

11.70

自引率

0.00%

发文量

期刊介绍： Statistics Surveys publishes survey articles in theoretical, computational, and applied statistics. The style of articles may range from reviews of recent research to graduate textbook exposition. Articles may be broad or narrow in scope. The essential requirements are a well specified topic and target audience, together with clear exposition. Statistics Surveys is sponsored by the American Statistical Association, the Bernoulli Society, the Institute of Mathematical Statistics, and by the Statistical Society of Canada.