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Recursive non-parametric kernel classification rule estimation for independent functional data

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  • Yousri Slaoui

    (Université de Poitiers)

Abstract

In this paper we propose an automatic selection of the bandwidth of the recursive non-parametric estimation of the kernel classification rule function defined by the stochastic approximation algorithm, when the explanatory data are curves and the response is categorical. We established a central limit theorem for our proposed recursive estimators, the proposed recursive estimators will be very competitive to the non-recursive one in terms of estimation error but much better in terms of computational costs. The proposed estimators are used first on simulated waveform curves and then on real phoneme data.

Suggested Citation

  • Yousri Slaoui, 2021. "Recursive non-parametric kernel classification rule estimation for independent functional data," Computational Statistics, Springer, vol. 36(1), pages 79-112, March.
    • Handle: RePEc:spr:compst:v:36:y:2021:i:1:d:10.1007_s00180-020-01024-9
    DOI: 10.1007/s00180-020-01024-9
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    References listed on IDEAS

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    1. Frédéric Ferraty & Ingrid Van Keilegom & Philippe Vieu, 2010. "On the Validity of the Bootstrap in Non‐Parametric Functional Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 37(2), pages 286-306, June.
    2. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
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    5. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    6. Delaigle, A. & Gijbels, I., 2004. "Practical bandwidth selection in deconvolution kernel density estimation," Computational Statistics & Data Analysis, Elsevier, vol. 45(2), pages 249-267, March.
    7. Slaoui, Yousri, 2019. "Wild bootstrap bandwidth selection of recursive nonparametric relative regression for independent functional data," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 494-511.
    8. Asma Jmaei & Yousri Slaoui & Wassima Dellagi, 2017. "Recursive distribution estimator defined by stochastic approximation method using Bernstein polynomials," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(4), pages 792-805, October.
    9. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    10. Ferraty, F. & Van Keilegom, Ingrid & Vieu, P., 2012. "Regression when both response and predictor are functions," LIDAM Reprints ISBA 2012004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Kara, Lydia-Zaitri & Laksaci, Ali & Rachdi, Mustapha & Vieu, Philippe, 2017. "Data-driven kNN estimation in nonparametric functional data analysis," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 176-188.
    12. Ferraty, Frederic & Van Keilegom, Ingrid & Vieu, Philippe, 2010. "On the Validity of the Bootstrap in Non-Parametric Functional Regression," LIDAM Reprints ISBA 2010018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
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