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August 1996 Orthogonalization of multivariate location estimators: the orthomedian
Rudolf Grübel
Ann. Statist. 24(4): 1457-1473 (August 1996). DOI: 10.1214/aos/1032298277


The coordinatewise median of a multivariate data set is a highly robust location estimator, but it depends on the choice of coordinates. A popular alternative which avoids this drawback is the spatial median, defined as the value that minimizes the sum of distances to the individual data points. In this paper we introduce and discuss another orthogonal equivariant version of the multivariate median, obtained by averaging the coordinatewise median over all orthogonal transformations. We investigate the asymptotic behavior of this estimator and compare it to the spatial median.


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Rudolf Grübel. "Orthogonalization of multivariate location estimators: the orthomedian." Ann. Statist. 24 (4) 1457 - 1473, August 1996.


Published: August 1996
First available in Project Euclid: 17 September 2002

zbMATH: 0867.62048
MathSciNet: MR1416642
Digital Object Identifier: 10.1214/aos/1032298277

Primary: 62F35 , 62H12

Keywords: asymptotic normality , multivariate median , orthogonal equivariance , robust estimation

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 4 • August 1996
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