Semiparametric regression for measurement error model with heteroscedastic error

Mengyan Li, Yanyuan Ma, Runze Li

Research output: Contribution to journalArticle

Abstract

Covariate measurement error is a common problem. Improper treatment of measurement errors may affect the quality of estimation and the accuracy of inference. Extensive literature exists on homoscedastic measurement error models, but little research exists on heteroscedastic measurement. In this paper, we consider a general parametric regression model allowing for a covariate measured with heteroscedastic error. We allow both the variance function of the measurement errors and the conditional density function of the error-prone covariate given the error-free covariates to be completely unspecified. We treat the variance function using B-spline approximation and propose a semiparametric estimator based on efficient score functions to deal with the heteroscedasticity of the measurement error. The resulting estimator is consistent and enjoys good inference properties. Its finite-sample performance is demonstrated through simulation studies and a real data example.

Original languageEnglish (US)
Pages (from-to)320-338
Number of pages19
JournalJournal of Multivariate Analysis
Volume171
DOIs
StatePublished - May 1 2019

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Heteroscedastic Errors
Semiparametric Regression
Measurement Error Model
Measurement errors
Measurement Error
Covariates
Variance Function
Parametric Regression
Estimator
Heteroscedasticity
Conditional Density
Spline Approximation
Score Function
Parametric Model
B-spline
Density Function
Regression Model
Splines
Probability density function
Simulation Study

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Numerical Analysis
  • Statistics, Probability and Uncertainty

Cite this

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abstract = "Covariate measurement error is a common problem. Improper treatment of measurement errors may affect the quality of estimation and the accuracy of inference. Extensive literature exists on homoscedastic measurement error models, but little research exists on heteroscedastic measurement. In this paper, we consider a general parametric regression model allowing for a covariate measured with heteroscedastic error. We allow both the variance function of the measurement errors and the conditional density function of the error-prone covariate given the error-free covariates to be completely unspecified. We treat the variance function using B-spline approximation and propose a semiparametric estimator based on efficient score functions to deal with the heteroscedasticity of the measurement error. The resulting estimator is consistent and enjoys good inference properties. Its finite-sample performance is demonstrated through simulation studies and a real data example.",
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Semiparametric regression for measurement error model with heteroscedastic error. / Li, Mengyan; Ma, Yanyuan; Li, Runze.

In: Journal of Multivariate Analysis, Vol. 171, 01.05.2019, p. 320-338.

Research output: Contribution to journalArticle

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