Asymptotic behaviour of S-estimates of multivariate location parameters and dispersion matrices (Q1103299)

Random vectors of dimension \(k\geq 2\) are considered, when their common density is given by \(| \Sigma |^{-}f((x-\mu)^ t\Sigma^{- 1}(x-\mu))\). The problem is to obtain affine equivariant estimators of \(\mu\) and \(\Sigma\), with high breakdown points. The minimum volume estimators proposed by \textit{P. J. Rousseeuw} [Mathematical statistics and applications, Proc. 4th Pannonian Symp. Math. Stat., Bad Tatzmannsdorf/Austria 1983, Vol. B, 283-297 (1985; Zbl 0609.62054)] and other S-estimators are considered. Under certain differentiability conditions the estimates are consistent and asymptotically normally distributed with a norming factor of \(n^{1/2}\). Two final sections of the paper contain an analysis of the breakdown point and an example.