ON AN ADAPTIVE TRANSFORMATION RETRANSFORMATION ESTIMATE OF MULTIVARIATE LOCATION

An affine equivariant estimate of multivariate location based on an adaptive transformation and retransformation approach has been studied. The work is primarily motivated by earlier work on different versions of multivariate median and their properties. We have tried to explore an issue related to efficiency and equivariance that was originally raised by Bickel ( Annals of Mathematical Statistics , 1964) and subsequently investigated by Brown and Hettmansperger ( Journal of the Royal Statistical Society, 1987, 1989). It has been shown that our estimate has better asymptotic performance than the vector of coordinatewise medians when the variables are substantially correlated. Finite sample performance of the estimate is investigated using Monte Carlo simulations. Some examples are presented to demonstrate the effect of adaptive transformation retransformation strategy in the construction of multivariate location estimates for real data.

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