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Nonparametric recursive estimation of the derivative of the regression function with application to sea shores water quality

Author

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  • Bernard Bercu

    (Université de Bordeaux)

  • Sami Capderou

    (Université de Bordeaux)

  • Gilles Durrieu

    (Université de Bretagne Sud
    Université de la Nouvelle-Calédonie)

Abstract

This paper is devoted to the nonparametric estimation of the derivative of the regression function in a nonparametric regression model. We implement a very efficient and easy to handle statistical procedure based on the derivative of the recursive Nadaraya–Watson estimator. We establish the almost sure convergence as well as the asymptotic normality for our estimates. We also illustrate our nonparametric estimation procedure on simulated data and real life data associated with sea shores water quality and valvometry.

Suggested Citation

  • Bernard Bercu & Sami Capderou & Gilles Durrieu, 2019. "Nonparametric recursive estimation of the derivative of the regression function with application to sea shores water quality," Statistical Inference for Stochastic Processes, Springer, vol. 22(1), pages 17-40, April.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:1:d:10.1007_s11203-017-9169-1
    DOI: 10.1007/s11203-017-9169-1
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    References listed on IDEAS

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    5. Blondin, David, 2007. "Rates of strong uniform consistency for local least squares kernel regression estimators," Statistics & Probability Letters, Elsevier, vol. 77(14), pages 1526-1534, August.
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