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Semiparametric regression for measurement error model with heteroscedastic error

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  • Li, Mengyan
  • Ma, Yanyuan
  • Li, Runze

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.

Suggested Citation

  • Li, Mengyan & Ma, Yanyuan & Li, Runze, 2019. "Semiparametric regression for measurement error model with heteroscedastic error," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 320-338.
    • Handle: RePEc:eee:jmvana:v:171:y:2019:i:c:p:320-338
    DOI: 10.1016/j.jmva.2018.12.012
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    References listed on IDEAS

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    1. Abhra Sarkar & Bani K. Mallick & Raymond J. Carroll, 2014. "Bayesian semiparametric regression in the presence of conditionally heteroscedastic measurement and regression errors," Biometrics, The International Biometric Society, vol. 70(4), pages 823-834, December.
    2. Devanarayan, Viswanath & Stefanski, Leonard A., 2002. "Empirical simulation extrapolation for measurement error models with replicate measurements," Statistics & Probability Letters, Elsevier, vol. 59(3), pages 219-225, October.
    3. Staudenmayer, John & Ruppert, David & Buonaccorsi, John P., 2008. "Density Estimation in the Presence of Heteroscedastic Measurement Error," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 726-736, June.
    4. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    5. Berry S. M. & Carroll R. J & Ruppert D., 2002. "Bayesian Smoothing and Regression Splines for Measurement Error Problems," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 160-169, March.
    6. Bertrand, A. & Legrand, C. & Léonard, D. & Van Keilegom, I., 2017. "Robustness of estimation methods in a survival cure model with mismeasured covariates," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 3-18.
    7. Bertrand, Aurelie & Legrand, Catherine & Leonard, Daniel & Van Keilegom, Ingrid, 2017. "Robustness of estimation methods in a survival cure model with mismeasured covariates," LIDAM Reprints ISBA 2017021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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    Cited by:

    1. Michal Pešta, 2021. "Changepoint in Error-Prone Relations," Mathematics, MDPI, vol. 9(1), pages 1-25, January.
    2. Roberto Mari & Antonello Maruotti, 2022. "A two-step estimator for generalized linear models for longitudinal data with time-varying measurement error," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 273-300, June.
    3. Zhang, Yuexia & Qin, Guoyou & Zhu, Zhongyi & Zhang, Jiajia, 2022. "Empirical likelihood inference for longitudinal data with covariate measurement errors: An application to the LEAN study," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).

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