The Behavior of the Stahel-Donoho Robust Multivariate Estimator
研究了Stahel-Donoho多元位置和散度估计量的性质，通过加权均值和协方差矩阵实现高抗污染性，模拟显示其在正态和柯西分布下效率高，优于最小体积椭球估计量。
Abstract The Stahel-Donoho estimators (t, V) of multivariate location and scatter are defined as a weighted mean and a weighted covariance matrix with weights of the form w(r), where w is a weight function and r is a measure of “outlyingness,” obtained by considering all univariate projections of the data. It has a high breakdown point for all dimensions and order √n consistency. The asymptotic bias of V for point mass contamination for suitable weight functions is compared with that of Rousseeuw's minimum volume ellipsoid (MVE) estimator. A simulation shows that for a suitable w, t and V exhibit high efficiency for both normal and Cauchy distributions and are better than their competitors for normal data with point-mass contamination. The performances of the estimators for detecting outliers are compared for both a real and a synthetic data set.