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Biometrika 2002 89(4):851-860; doi:10.1093/biomet/89.4.851
© 2002 by Biometrika Trust
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A practical affine equivariant multivariate median

Thomas P.Hettmansperger1 and Ronald H.Randles2

1 Department of Statistics, Pennsylvania State University, University Park, Pennsylvania 16802, U.S.Atph{at}stat.psu.edu 2 Department of Statistics, University of Florida, Gainesville, Florida 32611, U.S.A.rrandles{at}stat.ufl.edu

A robust affine equivariant estimator of location for multivariate data is proposed which becomes the univariate median for data of dimension one.The estimator is robust in the sense that it has a bounded influence function, a positive breakdown value and has high efficiency compared to the sample mean for heavy-tailed distributions. Perhaps its greatest strength is that, unlike other affine equivariant multivariate medians, it is easily computed for data in any practical dimension.

Key Words: Bounded influence; Breakdown; L1 median; Multivariate location estimate; Multivariate median; Oja median; Robust

Received January 2001. Revised May 2002


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