On a robust and effcient maximum depth estimator

作     者：ZUO YiJun1,2 & LAI ShaoYong1 1 School of Economic Mathematics,Southwestern University of Finance and Economics,Chengdu 610074,China 2 Department of Statistics and Probability,Michigan State University,East Lansing,MI 48823,USA 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2009年第52卷第6期

页      面：1212-1232页

学科分类：02[经济学] 0202[经济学-应用经济学] 020208[经济学-统计学] 07[理学] 0714[理学-统计学（可授理学、经济学学位）] 070103[理学-概率论与数理统计] 0701[理学-数学] 

基　　金：supported by Natural Science Foundation of USA (Grant Nos. DMS-0071976, DMS-0234078) the Southwestern University of Finance and Economics Third Period Construction Item Funds of the 211 Project (Grant No. 211D3T06) 

主　　题：data depth maximum depth estimator median location estimator breakdown point asymptotic distribution robustness effciency 

摘      要：The best breakdown point robustness is one of the most outstanding features of the univariate *** this robustness property,the median,however,has to pay the price of a low effciency at normal and other light-tailed *** equivariant multivariate analogues of the univariate median with high breakdown points were constructed in the past two *** the high breakdown robustness,most of them also have to sacrifice their effciency at normal and other models,*** affine equivariant maximum depth estimator proposed and studied in this paper turns out to be an *** the univariate median,it also possesses a highest breakdown point among all its multivariate *** the univariate median,it is also highly efficient relative to the sample mean at normal and various other distributions,overcoming the vital low-effciency shortcoming of the univariate and other multivariate generalized *** paper also studies the asymptotics of the estimator and establishes its limit distribution without symmetry and other strong assumptions that are typically imposed on the underlying distribution.