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 recursi...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.展开更多
Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w...Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.展开更多
A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and b...A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.展开更多
基金supported by the Natural Sciences and Engineering Research Council of Canadathe National Natural Science Foundation of China+2 种基金the Doctorial Fund of Education Ministry of Chinasupported by the Natural Sciences and Engineering Research Council of Canadasupported by the National Natural Science Foundation of China
文摘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.
文摘Given a positive definite matrix measure Ω supported on the unit circle T, then main purpose of this paper is to study the asymptotic behavior of L n()L n(Ω) -1 and Φ n(z;)Φ n(z;Ω) -1 where(z)=Ω(z)+Mδ(z-w); |w|>1,M is a positive definite matrix and δ is the Dirac matrix measure. Here, L n(·) means the leading coefficient of the orthonormal matrix polynomials Φ n(z;·). Finally, we deduce the asymptotic behavior of Φ n(w;)Φ n(w;Ω)* in the case when M=I.
基金This research is supported by the National Natural Science Foundation of China （Grant No. 10371012, 10231030,and 40574020）.
文摘A class of robust location estimators called weighted randomly trimmed means are introduced and not only their consistency and asymptotic normality are proved, but their influence functions, asymptotic variances and breakdown points are also derived. They possess the same breakdown points as the median, and some of them own higher asymptotic relative efficiencies at the heavy-tailed distributions than some other well-known location estimators; whereas the trimmed means, Winsorized means and Huber＇s M-estimator possess higher asymptotic relative efficiencies at the light-tailed distributions, in which Huber＇s M-estimator is the most robust.
