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Nonparametric regression for dependent data in the errors-in-variables problem

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  • Toshio Honda

Abstract

We consider the nonparametric estimation of the regression functions for dependent data. Suppose that the covariates are observed with additive errors in the data and we employ nonparametric deconvolution kernel techniques to estimate the regression functions in this paper. We investigate how the strength of time dependence affects the asymptotic properties of the local constant and linear estimators. We treat both short-range dependent and long-range dependent linear processes in a unified way and demonstrate that the long-range dependence (LRD) of the covariates affects the asymptotic properties of the nonparametric estimators as well as the LRD of regression errors does.

Suggested Citation

  • Toshio Honda, 2009. "Nonparametric regression for dependent data in the errors-in-variables problem," Global COE Hi-Stat Discussion Paper Series gd09-092, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hst:ghsdps:gd09-092
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    File URL: http://gcoe.ier.hit-u.ac.jp/research/discussion/2008/pdf/gd09-092.pdf
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    References listed on IDEAS

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    1. Harry Zanten & Pawel Zareba, 2008. "A note on wavelet density deconvolution for weakly dependent data," Statistical Inference for Stochastic Processes, Springer, vol. 11(2), pages 207-219, June.
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    Cited by:

    1. Igor S. Borisov & Yuliana Yu. Linke & Pavel S. Ruzankin, 2021. "Universal weighted kernel-type estimators for some class of regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(2), pages 141-166, February.
    2. Mynbaev, Kairat & Martins-Filho, Carlos, 2015. "Consistency and asymptotic normality for a nonparametric prediction under measurement errors," Journal of Multivariate Analysis, Elsevier, vol. 139(C), pages 166-188.

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