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

doi:10.1016/S0252-9602(10)60048-3

数学物理学报(英文版) ›› 2010, Vol. 30 ›› Issue (1): 319-329.doi: 10.1016/S0252-9602(10)60048-3

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

Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China

收稿日期:2006-10-13 修回日期:2007-12-10 出版日期:2010-01-20 发布日期:2010-01-20
基金资助:
The research of B. Q. Miao was partially supported by the Natural Sciences and Engineering Research Council of Canada, the National Natural Science Foundation of China and the Doctorial Fund of Education Ministry of China. The research of Y. Wu was partially supported by the Natural Sciences and Engineering Research Council of Canada. The research of Donghai Liu was partially supported by the National Natural Science Foundation of China.

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

Department of Statistics and Finance, University of Science and Technology of China, Hefei 230026, China

Received:2006-10-13 Revised:2007-12-10 Online:2010-01-20 Published:2010-01-20
Supported by:
The research of B. Q. Miao was partially supported by the Natural Sciences and Engineering Research Council of Canada, the National Natural Science Foundation of China and the Doctorial Fund of Education Ministry of China. The research of Y. Wu was partially supported by the Natural Sciences and Engineering Research Council of Canada. The research of Donghai Liu was partially supported by the National Natural Science Foundation of China.

摘要/Abstract

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 u₁(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, recursive algorithm, regression coefficients, robust stimation, regression model

Abstract:

Key words: asymptotic efficiency, asymptotic normality, asymptotic relative efficiency, least absolute deviation, least squares, M-estimation, multivariate linear, optimal estimator, recursive algorithm, regression coefficients, robust stimation, regression model

中图分类号:

62F10

缪柏其, 吴月华, 刘东海. LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES[J]. 数学物理学报(英文版), 2010, 30(1): 319-329.

MIAO Bai-Qi, WU Yue-Hua, LIU Dong-Hai. LIMITING BEHAVIOR OF RECURSIVE M-ESTIMATORS IN MULTIVARIATE LINEAR REGRESSION MODELS AND THEIR ASYMPTOTIC EFFICIENCIES[J]. Acta mathematica scientia,Series B, 2010, 30(1): 319-329.

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

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

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