L 1-Norm Estimation and Random Weighting Method in a Semiparametric Model

L 1-Norm Estimation and Random Weighting Method in a Semiparametric Model In this paper, the L 1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L 1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

L 1-Norm Estimation and Random Weighting Method in a Semiparametric Model

L 1-Norm Estimation and Random Weighting Method in a Semiparametric Model

Acta Mathematicae Applicatae Sinica, English Series Vol. 21, No. 2 (2005) 295–302 L L -Norm Estimation and Random Weighting Method in a Semiparametric Model 1 2 Liu-gen Xue ,Li-xing Zhu College of Applied Sciences, Beijing University of Technology, Beijing 100022, China (E-mail: lgxue@bjpu,edu.cn) Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences, Beijing 100080, China & University of Hong Kong, Hong Kong, China (E-mail: lzhu@hku.hk) Abstract In this paper, the L -norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L -norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method. Keywords L -norm estimation, random weighting method, semiparametric regression model 2000 MR Subject Classification 62G05, 62F12 1 Introduction In a semiparametric regression model, one observes (T ,X ,Y ), 1 ≤ i ≤ n of which the Y ’s i i i i are response variable depending on covariates (T ,X ) through the relationship i i Y = X β + g(T )+ e,i =, 1,··· ,n, (1.1) i i i where {(T ,X ,Y ), 1 ≤ i ≤ n} are independent and identically distributed (i.i.d.) as (T, X, Y ), i i i the covariate (T, X)is R × [0, 1] valued, β is a d-vector of unknown parametric, and g is an unknown smooth function on [0,1], {e , 1 ≤ i ≤ n} are i.i.d. random error which are independent of {(X ,T ), 1 ≤ i ≤ n}. i i [6] Model (1.1) was proposed and studied by Engle, Granger and Rice and has been exten- sively investigated in recent years. For example, see [2,8–10]. By use of piecewise polynomial to [2] approximate g,Chen acquired the...
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Publisher
Springer-Verlag
Copyright
Copyright © 2005 by Springer-Verlag Berlin Heidelberg
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
D.O.I.
10.1007/s10255-005-0237-8
Publisher site
See Article on Publisher Site

Abstract

In this paper, the L 1-norm estimators and the random weighted statistic for a semiparametric regression model are constructed, the strong convergence rates of estimators are obtain under certain conditions, the strong efficiency of the random weighting method is shown. A simulation study is conducted to compare the L 1-norm estimator with the least square estimator in term of approximate accuracy, and simulation results are given for comparison between the random weighting method and normal approximation method.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jan 1, 2005

References

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