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Generalized profile LSE in varying-coefficient partially linear models with measurement errors

Generalized profile LSE in varying-coefficient partially linear models with measurement errors This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Y i = X i t β + Z i t α(U i ) + ɛ i , W i = X i + ζ i , i = 1, …, n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Generalized profile LSE in varying-coefficient partially linear models with measurement errors

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References (22)

Publisher
Springer Journals
Copyright
Copyright © 2013 by Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and 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
DOI
10.1007/s10255-013-0229-z
Publisher site
See Article on Publisher Site

Abstract

This paper is concerned with the estimating problem of a semiparametric varying-coefficient partially linear errors-in-variables model Y i = X i t β + Z i t α(U i ) + ɛ i , W i = X i + ζ i , i = 1, …, n. Due to measurement errors, the usual profile least square estimator of the parametric component, local polynomial estimator of the nonparametric component and profile least squares based estimator of the error variance are biased and inconsistent. By taking the measurement errors into account we propose a generalized profile least squares estimator for the parametric component and show it is consistent and asymptotically normal. Correspondingly, the consistent estimation of the nonparametric component and error variance are proposed as well. These results may be used to make asymptotically valid statistical inferences. Some simulation studies are conducted to illustrate the finite sample performance of these proposed estimations.

Journal

Acta Mathematicae Applicatae Sinica – Springer Journals

Published: Nov 20, 2013

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