publication . Article . 1992

Bias-robust estimators of multivariate scatter based on projections

Maronna, Ricardo A; Stahel, Werner A; Yohai, Victor J;
Open Access English
  • Published: 01 Jul 1992 Journal: Journal of Multivariate Analysis, issue 1, pages 141-161 (issn: 0047259X, Copyright policy)
  • Publisher: Published by Elsevier Inc.
Abstract
AbstractEquivariant estimation of the multivariate scatter of a random vector X can be derived from a criterion of (lack of) spherical symmetry g(X). The scatter matrix is V = (ATA)−1, where A is the transformation matrix which makes AX as spherical as possible, that is, which minimizes g(AX). The new class of projection estimators is based on making the spread of univariate projections as constant as possible by choosing g(X) = sup|u| = 1 |s(uTX) −1|, where s is any robust scale functional. The breakdown point of such an estimator is at least that of s, independently of the dimension p of X. In order to study the bias, we calculate condition numbers based on as...
Subjects
free text keywords: robust estimation, projection estimator, high breakdown point estimation, covariance matrix, Statistics, Probability and Uncertainty, Statistics and Probability, Numerical Analysis, Scale parameter, Econometrics, Scatter matrix, Transformation matrix, Median absolute deviation, Statistics, Mathematics, Multivariate random variable, Estimator, Univariate
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