Bounds for the breakdown point of the simplicial median
type: Item
instance of: scholarly article
title: Bounds for the breakdown point of the simplicial median
zbMATH Open document ID: 0898.62041
author: Yanyan Li
published in: Journal of Multivariate Analysis
publication date: 1998-10-26T00:00:00Z
review text: \textit{R. Y. Liu} [Ann. Stat. 18, No. 1, 405-414 (1990; Zbl 0701.62063)] introduced the simplicial median as a generalization of the median for a multivariate probability distribution. The simplicial median is affine equivariant and so is the sample simplicial median if it is unique or if it is conveniently chosen when it is not unique. The object of this article is to prove that Liu's sample simplicial median and its modified version [\textit{M. A. Arcones} and \textit{E. Giné}, Ann. Probab. 21, No. 3, 1494-1542 (1993; Zbl 0789.60031)] are both robust. Their robustness will be measured by means of the finite sample breakdown point.
Mathematics Subject Classification ID: 62F35
Mathematics Subject Classification ID: 62H12
zbMATH DE Number: 844597
zbMATH Keywords: simplicial sample median
zbMATH Keywords: simplicial median
zbMATH Keywords: robustness
zbMATH Keywords: finite sample breakdown point
MaRDI profile type: Publication
full work available at URL: jmva.1995.1063
OpenAlex ID: W2080960092
DOI: 10.1006/JMVA.1995.1063
description: scientific article; zbMATH DE number 844597