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

Author

Listed:
  • 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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    1. Johnston, Gordon J., 1982. "Probabilities of maximal deviations for nonparametric regression function estimates," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 402-414, September.
    2. 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.
    3. Paul Deheuvels & David Mason, 2004. "General Asymptotic Confidence Bands Based on Kernel-type Function Estimators," Statistical Inference for Stochastic Processes, Springer, vol. 7(3), pages 225-277, October.
    4. Aboubacar Amiri, 2012. "Recursive regression estimators with application to nonparametric prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 169-186.
    5. Kazuo Noda, 1976. "Estimation of a regression function by the parzen kernel-type density estimators," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 28(1), pages 221-234, December.
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    Cited by:

    1. Senga Kiessé, Tristan & Durrieu, Gilles, 2024. "On a discrete symmetric optimal associated kernel for estimating count data distributions," Statistics & Probability Letters, Elsevier, vol. 208(C).

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