LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES  

作　　者：缪柏其 吴月华 刘东海 

机构地区：[1]Department of Statistics and Finance,University of Science and Technology of China [2]Department of Mathematics and Statistics,York University,Toronto,Ontario,Canada [3]Department of Fire Command,Chinese People's Armed Police Forces Academy

出　　处：《Acta Mathematica Scientia》2010年第1期319-329,共11页数学物理学报（B辑英文版）

基　　金：supported by the Natural Sciences and Engineering Research Council of Canada;the National Natural Science Foundation of China;the Doctorial Fund of Education Ministry of China;supported by the Natural Sciences and Engineering Research Council of Canada;supported by the National Natural Science Foundation of China

摘　　要：Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.Recursive algorithms are very useful for computing M-estimators of regression coefficients and scatter parameters. In this article, it is shown that for a nondecreasing ul （t）, under some mild conditions the recursive M-estimators of regression coefficients and scatter parameters are strongly consistent and the recursive M-estimator of the regression coefficients is also asymptotically normal distributed. Furthermore, optimal recursive M-estimators, asymptotic efficiencies of recursive M-estimators and asymptotic relative efficiencies between recursive M-estimators of regression coefficients are studied.

关 键 词：asymptotic efficiency asymptotic normality asymptotic relative efficiency least absolute deviation least squares M-ESTIMATION multivariate linear optimal estimator reeursive algorithm regression coefficients robust estimation regression model 

分 类 号：O212[理学—概率论与数理统计]