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An alternative local polynomial estimator for the error-in-variables problem

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  • Xianzheng Huang
  • Haiming Zhou

Abstract

We consider the problem of estimating a regression function when a covariate is measured with error. Using the local polynomial estimator of Delaigle et al. [(2009), ‘A Design-adaptive Local Polynomial Estimator for the Errors-in-variables Problem’, Journal of the American Statistical Association, 104, 348–359] as a benchmark, we propose an alternative way of solving the problem without transforming the kernel function. The asymptotic properties of the alternative estimator are rigorously studied. A detailed implementing algorithm and a computationally efficient bandwidth selection procedure are also provided. The proposed estimator is compared with the existing local polynomial estimator via extensive simulations and an application to the motorcycle crash data. The results show that the new estimator can be less biased than the existing estimator and is numerically more stable.

Suggested Citation

  • Xianzheng Huang & Haiming Zhou, 2017. "An alternative local polynomial estimator for the error-in-variables problem," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(2), pages 301-325, April.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:2:p:301-325
    DOI: 10.1080/10485252.2017.1303060
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    1. Delaigle, Aurore & Hall, Peter, 2008. "Using SIMEX for Smoothing-Parameter Choice in Errors-in-Variables Problems," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 280-287, March.
    2. Delaigle, Aurore & Fan, Jianqing & Carroll, Raymond J., 2009. "A Design-Adaptive Local Polynomial Estimator for the Errors-in-Variables Problem," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 348-359.
    3. Susanne M. Schennach, 2004. "Estimation of Nonlinear Models with Measurement Error," Econometrica, Econometric Society, vol. 72(1), pages 33-75, January.
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