Influence functions and asymptotic efficiency of the affine equivariant rank covariance matrix. Submitted (2002a). Sign and rank covariance matrices 13

Vis uri et al. (20Gl) proposed and illustrated the use ofthe affine equivariant rank covariance matrix (ReM) in classical multivariate inference problems. The ReM was shown to be asymptotically multinormal but explicit formulas for the limiting variances and covariances were not given yet. In this paper the influence functions and the limiting variances and covariances of the ReM and the corresponding scat-ter estimate are derived in the multivariate elliptic case. Limiting efficiencies are given in the multivariate normal and t distribution cases. The estimates based on the ReM are highly efficient in the multinormal case, and for heavy tailed distrib-ution, perform better than those based on the regular covariance matrix. Key words: Elliptic distribution; influence function; multivariate analysis; multi-variate rank; scatter matrix