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Statistica Sinica 18(2008), 405-424





ON CONSTRAINED M-ESTIMATION AND ITS RECURSIVE

ANALOG IN MULTIVARIATE LINEAR

REGRESSION MODELS


Zhidong Bai$^{1,2}$, Xiru Chen$^3$ and Yuehua Wu$^4$


$^1$Northeast Normal University, $^2$National University of Singapore,

$^3$Graduate University of the Chinese Academy of Sciences and $^4$York University


Abstract: In this paper, the constrained M-estimation of the regression coefficients and scatter parameters in a multivariate linear regression model is considered. Robustness and asymptotic behavior are investigated. Since constrained M-estimation is not easy to compute, an up-dating recursion procedure is proposed to simplify the computation of the estimators when a new observation is obtained. We show that, under mild conditions, the recursion estimates are strongly consistent. A Monte Carlo simulation study of the recursion estimates is also provided.



Key words and phrases: Asymptotic normality, breakdown point, consistency, constrained M-estimation, influence function, linear model, M-estimation, recursion estimation, robust estimation.

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