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

DOI:
https://doi.org/10.1090/S0002-9939-96-03657-X

MathSciNet review:
1363452

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-96-03657-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