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Smooth backfitting for errors-in-variables varying coefficient regression models

Author

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  • Han, Kyunghee
  • Lee, Young K.
  • Park, Byeong U.

Abstract

Varying coefficient models inherit the simplicity and easy interpretation of classical linear models while enjoying the flexibility of nonparametric models. They are very useful in analyzing the relation between a response and a set of predictors. There has been no study, however, on the estimation of varying coefficients when the predictors, on which the varying coefficients depend, are contaminated by measurement errors. A new kernel smoothing technique that is tailored to the structure of an underlying varying coefficient model as well as corrects for the bias due to the measurement errors is developed here. The estimators of the varying coefficients are given implicitly by solving a system of integral equations, whose implementation requires an iterative backfitting procedure. The existence of a unique solution and the convergence of the associated backfitting algorithm are established theoretically. Some numerical evidences that support the theory and demonstrate the success of the proposed methodology are presented.

Suggested Citation

  • Han, Kyunghee & Lee, Young K. & Park, Byeong U., 2020. "Smooth backfitting for errors-in-variables varying coefficient regression models," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    • Handle: RePEc:eee:csdana:v:145:y:2020:i:c:s0167947319302646
    DOI: 10.1016/j.csda.2019.106909
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    References listed on IDEAS

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    1. Yang, Lijian & Park, Byeong U. & Xue, Lan & Hardle, Wolfgang, 2006. "Estimation and Testing for Varying Coefficients in Additive Models With Marginal Integration," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1212-1227, September.
    2. Byeong U. Park & Enno Mammen & Young K. Lee & Eun Ryung Lee, 2015. "Varying Coefficient Regression Models: A Review and New Developments," International Statistical Review, International Statistical Institute, vol. 83(1), pages 36-64, April.
    3. Liang Li & Tom Greene, 2008. "Varying Coefficients Model with Measurement Error," Biometrics, The International Biometric Society, vol. 64(2), pages 519-526, June.
    4. Oliver Linton & E. Mammen & J. Nielsen, 1997. "The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions," Cowles Foundation Discussion Papers 1160, Cowles Foundation for Research in Economics, Yale University.
    5. Fan, Jianqing & Masry, Elias, 1992. "Multivariate regression estimation with errors-in-variables: Asymptotic normality for mixing processes," Journal of Multivariate Analysis, Elsevier, vol. 43(2), pages 237-271, November.
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