Asymptotic distributions of the maximal depth estimators for regression and multivariate location
回归与多变量位置最大深度估计量的渐近分布
We derive the asymptotic distribution ofthe maximal depth regression estimator recently proposed in Rousseeuw and Hubert. The estimator is obtained by maximizing a projection-based depth and the limiting distribution is characterized through a max–min operation of a continuous process. The same techniques can be used to obtain the limiting distribution of some other depth estimators including Tukey’s deepest point based on half-space depth. Results for the special case of…