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On an adaptive transformation–retransformation estimate of multivariate location
Authors:Biman Chakraborty,&   Probul Chaudhuri
Affiliation:Indian Statistical Institute, Calcutta, India
Abstract:An affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach is studied. The work is primarily motivated by earlier work on different versions of the multivariate median and their properties. We explore an issue related to efficiency and equivariance that was originally raised by Bickel and subsequently investigated by Brown and Hettmansperger. Our estimate has better asymptotic performance than the vector of co-ordinatewise medians when the variables are substantially correlated. The finite sample performance of the estimate is investigated by using Monte Carlo simulations. Some examples are presented to demonstrate the effect of the adaptive transformation–retransformation strategy in the construction of multivariate location estimates for real data.
Keywords:Affine transformation    Asymptotic efficiency    Equivariance    Generalized variance    Multivariate median
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