A Distribution-Free $M$-Estimator of Multivariate Scatter

摘要: The existence and uniqueness of a limiting form Huber-type $M$-estimator multivariate scatter is established under certain conditions on the observed sample. These hold with probability one when sampling randomly from continuous distribution. estimator proven by showing that it point specific algorithm. Hence, proof constructive. For populations, shown to be strongly consistent asymptotically normal. An important property its asymptotic distribution distribution-free respect class elliptically distributed populations. This also holds for finite sample size location parameter known. In addition, "most robust" matrix an elliptical in sense minimizing maximum variance.