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Difference based estimation for partially linear regression models with measurement errors

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  • Zhao, Haibing
  • You, Jinhong

Abstract

This paper is concerned with the estimating problem of the partially linear regression models where the linear covariates are measured with additive errors. A difference based estimation is proposed to estimate the parametric component. We show that the resulting estimator is asymptotically unbiased and achieves the semiparametric efficiency bound if the order of the difference tends to infinity. The asymptotic normality of the resulting estimator is established as well. Compared with the corrected profile least squares estimation, the proposed procedure avoids the bandwidth selection. In addition, the difference based estimation of the error variance is also considered. For the nonparametric component, the local polynomial technique is implemented. The finite sample properties of the developed methodology is investigated through simulation studies. An example of application is also illustrated.

Suggested Citation

  • Zhao, Haibing & You, Jinhong, 2011. "Difference based estimation for partially linear regression models with measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1321-1338, November.
    • Handle: RePEc:eee:jmvana:v:102:y:2011:i:10:p:1321-1338
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    References listed on IDEAS

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    1. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-954, July.
    2. Aneiros-Perez, G. & Vilar-Fernandez, J.M., 2008. "Local polynomial estimation in partial linear regression models under dependence," Computational Statistics & Data Analysis, Elsevier, vol. 52(5), pages 2757-2777, January.
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    5. Hamilton, Scott A. & Truong, Young K., 1997. "Local Linear Estimation in Partly Linear Models," Journal of Multivariate Analysis, Elsevier, vol. 60(1), pages 1-19, January.
    6. Hua Liang & Suojin Wang & Raymond J. Carroll, 2007. "Partially linear models with missing response variables and error-prone covariates," Biometrika, Biometrika Trust, vol. 94(1), pages 185-198.
    7. Yatchew, A., 1997. "An elementary estimator of the partial linear model," Economics Letters, Elsevier, vol. 57(2), pages 135-143, December.
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    Cited by:

    1. Hongchang Hu & Yu Zhang & Xiong Pan, 2016. "Asymptotic normality of DHD estimators in a partially linear model," Statistical Papers, Springer, vol. 57(3), pages 567-587, September.
    2. Yuejin Zhou & Yebin Cheng & Wenlin Dai & Tiejun Tong, 2018. "Optimal difference-based estimation for partially linear models," Computational Statistics, Springer, vol. 33(2), pages 863-885, June.

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