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Recursive regression estimators with application to nonparametric prediction

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  • Aboubacar Amiri

Abstract

In the case of dependent data, the purpose of this paper is to establish the exact asymptotic quadratic error of a parametric family of recursive kernel regression estimators. Based on this family of estimators, recursive nonparametric kernel predictors are studied. For mixing Markov processes, their almost sure convergence to the best predictor is established. Efficiency of these methods is also shown through numerical simulations highlighting their significantly reduced time of computation.

Suggested Citation

  • Aboubacar Amiri, 2012. "Recursive regression estimators with application to nonparametric prediction," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 169-186.
    • Handle: RePEc:taf:gnstxx:v:24:y:2012:i:1:p:169-186
    DOI: 10.1080/10485252.2011.626855
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    Cited by:

    1. Aboubacar Amiri & Baba Thiam, 2018. "Regression estimation by local polynomial fitting for multivariate data streams," Statistical Papers, Springer, vol. 59(2), pages 813-843, June.
    2. Aboubacar Amiri, 2013. "Asymptotic normality of recursive estimators under strong mixing conditions," Statistical Inference for Stochastic Processes, Springer, vol. 16(2), pages 81-96, July.
    3. Amiri, Aboubacar & Crambes, Christophe & Thiam, Baba, 2014. "Recursive estimation of nonparametric regression with functional covariate," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 154-172.
    4. 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.
    5. Said Attaoui & Nengxiang Ling, 2016. "Asymptotic results of a nonparametric conditional cumulative distribution estimator in the single functional index modeling for time series data with applications," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 79(5), pages 485-511, July.

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