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B-spline estimation of regression functions with errors in variable

Author

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  • Koo, Ja-Yong
  • Lee, Kee-Won

Abstract

This paper proposes a new B-spline method for nonparametric regression function estimation which can be applied to the case even when the covariate is contaminated with noise. A property of B-splines, reproducing line property, is crucial in the construction of B-spline estimators for regression function. To account for errors in covariate, deconvolution is involved in the construction of B-spline estimators. It is shown that the B-spline estimators achieve the optimal rate of convergence which depends on the tail behavior of the characteristic function of the error distribution.

Suggested Citation

  • Koo, Ja-Yong & Lee, Kee-Won, 1998. "B-spline estimation of regression functions with errors in variable," Statistics & Probability Letters, Elsevier, vol. 40(1), pages 57-66, September.
    • Handle: RePEc:eee:stapro:v:40:y:1998:i:1:p:57-66
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    References listed on IDEAS

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    1. Breiman, Leo, 1993. "Fitting additive models to regression data : Diagnostics and alternative views," Computational Statistics & Data Analysis, Elsevier, vol. 15(1), pages 13-46, January.
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    Cited by:

    1. 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.
    2. Comte, F. & Lacour, C. & Rozenholc, Y., 2010. "Adaptive estimation of the dynamics of a discrete time stochastic volatility model," Journal of Econometrics, Elsevier, vol. 154(1), pages 59-73, January.

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