# 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

, Volume 21 (2) – Jan 1, 2005

## 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 Journals
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

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