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AStA Advances in Statistical Analysis

, Volume 98, Issue 2, pp 165–195 | Cite as

Asymptotic normality of estimators in heteroscedastic errors-in-variables model

  • Jing-Jing Zhang
  • Han-Ying LiangEmail author
  • Amei Amei
Original Paper
  • 291 Downloads

Abstract

This article is concerned with the estimating problem of heteroscedastic partially linear errors-in-variables models. We derive the asymptotic normality for estimators of the slope parameter and the nonparametric component in the case of known error variance with stationary \(\alpha \)-mixing random errors. Also, when the error variance is unknown, the asymptotic normality for the estimators of the slope parameter and the nonparametric component as well as variance function is considered under independent assumptions. Finite sample behavior of the estimators is investigated via simulations too.

Keywords

Partially linear errors-in-variables model Heteroscedastic Ordinary least-squares estimator Weighted ordinary least-squares estimator Asymptotic normality \(\alpha \)-mixing 

Mathematics Subject Classifications (2000)

62J12 62E20 

Notes

Acknowledgments

The authors were supported by the National Natural Science Foundation of China (11271286) and the Specialized Research Fund for the Doctor Program of Higher Education of China (20120072110007).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.College of ScienceUniversity of Shanghai for Science and TechnologyShanghaiPeople’s Republic of China
  2. 2.Department of MathematicsTongji UniversityShanghaiPeople’s Republic of China
  3. 3.Department of Mathematical SciencesUniversity of Nevada Las VegasLas VegasUSA

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