OPERATING TRANSFORMATION RETRANSFORMATION ON SPATIAL MEDIAN AND ANGLETEST

An affine equivariant modification of the spatial median constructed u sing an adaptive transformation and retransformation procedure has bee n studied. It has been shown that this new estimate of multivariate lo cation improves upon the performance of nonequivariant spatial median especially when there are correlations among the real valued component s of multivariate data as well as when the scales of those components are different (e.g. when data points follow an elliptically symmetric distribution). For such correlated multivariate data the proposed esti mate is more efficient than the non-equivariant vector of coordinatewi se sample medians, and it outperforms the sample mean vector in the ca se of heavy tailed non-normal distributions. As an extension of the me thodology, we have proposed an affine invariant modification of the we ll-known angle test based on the transformation approach, which is app licable to one sample multivariate location problems. We have observed that this affine invariant test performs better than the noninvariant angle test and the coordinatewise sign test for correlated multivaria te data. Also, for heavy tailed non-normal multivariate distributions, the test outperforms Hotelling's T-2 test. Finite sample performance of the proposed estimate and the test is investigated using Monte Carl o simulations. Some data analytic examples are presented to demonstrat e the implementation of the methodology in practice.