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Statistical inference for partially linear regression models with measurement errors

In this paper, the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors. Firstly, a bandwidth selection procedure is proposed, which is a combination of the difference-based technique and GCV method. Seco... Full description

Journal Title: Chinese Annals of Mathematics Series B, 2008, Vol.29(2), pp.207-222
Main Author: You, Jinhong
Other Authors: Xu, Qinfeng , Zhou, Bin
Format: Electronic Article Electronic Article
Language: English
Subjects:
ID: ISSN: 0252-9599 ; E-ISSN: 1860-6261 ; DOI: 10.1007/s11401-006-0210-8
Link: http://dx.doi.org/10.1007/s11401-006-0210-8
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recordid: springer_jour10.1007/s11401-006-0210-8
title: Statistical inference for partially linear regression models with measurement errors
format: Article
creator:
  • You, Jinhong
  • Xu, Qinfeng
  • Zhou, Bin
subjects:
  • Partially linear model
  • Measurement error
  • Bandwidth selection
  • Goodness-of-fit test
  • Oracle property
ispartof: Chinese Annals of Mathematics, Series B, 2008, Vol.29(2), pp.207-222
description: In this paper, the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors. Firstly, a bandwidth selection procedure is proposed, which is a combination of the difference-based technique and GCV method. Secondly, a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique. Thirdly, a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares. Same as “Variable selection via nonconcave penalized likelihood and its oracle properties” (J. Amer. Statist. Assoc., 96 , 2001, 1348–1360), it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function. Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.
language: eng
source:
identifier: ISSN: 0252-9599 ; E-ISSN: 1860-6261 ; DOI: 10.1007/s11401-006-0210-8
fulltext: fulltext
issn:
  • 1860-6261
  • 18606261
  • 0252-9599
  • 02529599
url: Link


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subjectPartially linear model ; Measurement error ; Bandwidth selection ; Goodness-of-fit test ; Oracle property
descriptionIn this paper, the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors. Firstly, a bandwidth selection procedure is proposed, which is a combination of the difference-based technique and GCV method. Secondly, a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique. Thirdly, a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares. Same as “Variable selection via nonconcave penalized likelihood and its oracle properties” (J. Amer. Statist. Assoc., 96 , 2001, 1348–1360), it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function. Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.
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abstractIn this paper, the authors investigate three aspects of statistical inference for the partially linear regression models where some covariates are measured with errors. Firstly, a bandwidth selection procedure is proposed, which is a combination of the difference-based technique and GCV method. Secondly, a goodness-of-fit test procedure is proposed, which is an extension of the generalized likelihood technique. Thirdly, a variable selection procedure for the parametric part is provided based on the nonconcave penalization and corrected profile least squares. Same as “Variable selection via nonconcave penalized likelihood and its oracle properties” (J. Amer. Statist. Assoc., 96 , 2001, 1348–1360), it is shown that the resulting estimator has an oracle property with a proper choice of regularization parameters and penalty function. Simulation studies are conducted to illustrate the finite sample performances of the proposed procedures.
copBerlin/Heidelberg
pubSpringer-Verlag
doi10.1007/s11401-006-0210-8
pages207-222
date2008-03