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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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


Authors: Biman Chakraborty and Probal Chaudhuri
Journal: Proc. Amer. Math. Soc. 124 (1996), 2539-2547
MSC (1991): Primary 62A05, 62H12; Secondary 62E20
MathSciNet review: 1363452
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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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Additional Information

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: http://dx.doi.org/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
Article copyright: © Copyright 1996 American Mathematical Society