Asymptotic expansion of S-estimators of location and covariance

By means of a straightforward application of empirical process theory, we show that S-estimators of multivariate location and covariance are asymptotically equivalent to a sum of independent vector and matrix valued random elements respectively. This provides an alternative proof of asymptotic normality of S-estimators and clearly explains the limiting covariance structure. It also leads to a relatively simple proof of asymptotic normality of the length of the shortest alpha-fraction.