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

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

Abstract

Abstract:

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.

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

CLC Number:

62F10

Cite this article

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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