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On an adaptive transformation–retransformation estimate of multivariate location

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  • Biman Chakraborty
  • Probul Chaudhuri

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.

Suggested Citation

  • Biman Chakraborty & Probul Chaudhuri, 1998. "On an adaptive transformation–retransformation estimate of multivariate location," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(1), pages 145-157.
    • Handle: RePEc:bla:jorssb:v:60:y:1998:i:1:p:145-157
    DOI: 10.1111/1467-9868.00114
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    Cited by:

    1. Shu, Lei & Chen, Yu & Zhang, Weiping & Wang, Xueqin, 2022. "Spatial rank-based high-dimensional change point detection via random integration," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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