Proceedings of the American Mathematical Society

On a transformation and re-transformation technique for constructing an affine equivariant multivariate median

Author(s): Biman Chakraborty; Probal Chaudhuri
Journal: Proc. Amer. Math. Soc. 124 (1996), 2539-2547.
MSC (1991): Primary 62A05, 62H12; Secondary 62E20
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Abstract: An affine equivariant version of multivariate median is introduced. The proposed median is easy to compute and has some appealing geometric features that are related to the configuration of a multivariate data cloud. The transformation and re-transformation approach used in the construction of the median has some fundamental connection with the data driven co-ordinate system considered by Chaudhuri and Sengupta (1993, Journal of the American Statistical Association). Large sample statistical properties of the median are discussed and finite sample performance is investigated using Monte Carlo simulations.

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Biman Chakraborty
Affiliation: Division of Theoretical Statistics & Mathematics, Indian Statistical Institute, 203 B. T. Road, Calcutta, 700035, India
Email: res9421@isical.ernet.in

Probal Chaudhuri
Affiliation: Division of Theoretical Statistics & Mathematics, Indian Statistical Institute, 203 B. T. Road, Calcutta, 700035, India
Email: probal@isical.ernet.in

DOI: 10.1090/S0002-9939-96-03657-X
PII: S 0002-9939(96)03657-X
Keywords: Affine transformation, asymptotic distribution, equivariance, generalized variance
Received by editor(s): November 18, 1994
Communicated by: Wei Y. Loh
Copyright of article: Copyright 1996, American Mathematical Society

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