Nonparametric regression function estimation for errors-in-variables models with validation data

Lilun Du; Changliang Zou; Zhaojun Wang

doi:10.5705/ss.2009.047

Nonparametric regression function estimation for errors-in-variables models with validation data

Lilun Du
, Changliang Zou
, Zhaojun Wang

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

9 Citations (Scopus)

Abstract

This paper develops an estimation approach for nonparametric regression analysis with measurement error in covariates, assuming the availability of independent validation data on them, in addition to primary data on the response variable and surrogate covariates. Without specifying any error model structure between the surrogate and true covariates, we propose an estimator that integrates local linear regression and Fourier transformation methods. Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.

Original language	English
Pages (from-to)	1093-1113
Journal	Statistica Sinica
Volume	21
Issue number	3
DOIs	https://doi.org/10.5705/ss.2009.047
Publication status	Published - Jul 2011
Externally published	Yes

Bibliographical note

Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

Funding

This research was supported by the NSF of Tianjin Grant 07JCYBJC04300, the NNSF of China Grants 10771107, 10711120448, 11071128 and 11001138.

Research Keywords

Asymptotic normality
Local linear regression
Measurement error
Trigonometric series

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title = "Nonparametric regression function estimation for errors-in-variables models with validation data",

abstract = "This paper develops an estimation approach for nonparametric regression analysis with measurement error in covariates, assuming the availability of independent validation data on them, in addition to primary data on the response variable and surrogate covariates. Without specifying any error model structure between the surrogate and true covariates, we propose an estimator that integrates local linear regression and Fourier transformation methods. Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.",

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AU - Du, Lilun

AU - Zou, Changliang

AU - Wang, Zhaojun

N1 - Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].

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N2 - This paper develops an estimation approach for nonparametric regression analysis with measurement error in covariates, assuming the availability of independent validation data on them, in addition to primary data on the response variable and surrogate covariates. Without specifying any error model structure between the surrogate and true covariates, we propose an estimator that integrates local linear regression and Fourier transformation methods. Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.

AB - This paper develops an estimation approach for nonparametric regression analysis with measurement error in covariates, assuming the availability of independent validation data on them, in addition to primary data on the response variable and surrogate covariates. Without specifying any error model structure between the surrogate and true covariates, we propose an estimator that integrates local linear regression and Fourier transformation methods. Under mild conditions, the consistency of the proposed estimator is established and the convergence rate is also obtained. Numerical examples show that it performs well in applications.

KW - Asymptotic normality

KW - Local linear regression

KW - Measurement error

KW - Trigonometric series

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DO - 10.5705/ss.2009.047

M3 - RGC 21 - Publication in refereed journal

SN - 1017-0405

VL - 21

SP - 1093

EP - 1113

JO - Statistica Sinica

JF - Statistica Sinica

IS - 3

ER -

Nonparametric regression function estimation for errors-in-variables models with validation data

Abstract

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Research Keywords

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