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Extrapolation estimation in parametric regression models with measurement error

Author

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  • Ayub, Kanwal
  • Song, Weixing
  • Shi, Jianhong

Abstract

For the general parametric regression models with covariates contaminated with normal measurement errors, an alternative method to the traditional simulation extrapolation algorithm is proposed to estimate the unknown parameters in the regression function. By applying the conditional expectation directly to the target function, the proposed algorithm successfully removes the simulation step, by generating an estimation equation either for immediate use or for extrapolating, thus providing a possibility of reducing the computational time or the Monte Carlo simulation error. Large sample properties of the resulting estimator, including the consistency and the asymptotic normality, are thoroughly discussed. Potential wide applications of the proposed estimation procedure are illustrated by examples, simulation studies, as well as a real data analysis.

Suggested Citation

  • Ayub, Kanwal & Song, Weixing & Shi, Jianhong, 2022. "Extrapolation estimation in parametric regression models with measurement error," Computational Statistics & Data Analysis, Elsevier, vol. 172(C).
    • Handle: RePEc:eee:csdana:v:172:y:2022:i:c:s0167947322000585
    DOI: 10.1016/j.csda.2022.107478
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    References listed on IDEAS

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    1. Chen, Kani & Guo, Shaojun & Lin, Yuanyuan & Ying, Zhiliang, 2010. "Least Absolute Relative Error Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1104-1112.
    2. Chen, Kani & Lin, Yuanyuan & Wang, Zhanfeng & Ying, Zhiliang, 2016. "Least product relative error estimation," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 91-98.
    3. Feng, Long & Zou, Changliang & Wang, Zhaojun, 2012. "Local Walsh-average regression," Journal of Multivariate Analysis, Elsevier, vol. 106(C), pages 36-48.
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