ABSTRACT
One serious drawback of coordinatewise sign as well as rank tests is that they are not invariant under arbitrary affine transformations of the data. In addition to being an undesirable geometric feature, this lack of invariance is known to have some negative impact on the statistical performance of these tests, especially when the real-valued components of the multivariate data are substantially correlated. This is also a handicap for both coordinatewise median and HL-estimates, as none of them is equivariant under affine transformation of the data. This issue was first raised by Bickel (1964, 1965), and subsequently investigated by Brown and Hettmansperger (1987, 1989).
