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Wild bootstrap bandwidth selection of recursive nonparametric relative regression for independent functional data

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  • Slaoui, Yousri

Abstract

We propose and investigate a new kernel regression estimator based on the minimization of the mean squared relative error. We study the properties of the proposed recursive estimator and compare it with the recursive estimator based on the minimization of the mean squared error proposed by Slaoui (2018). It turns out that, with an adequate choice of the parameters, the proposed estimator performs better than the recursive estimator based on the minimization of the mean squared error. We illustrate these theoretical results through a real chemometric dataset.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:173:y:2019:i:c:p:494-511
    DOI: 10.1016/j.jmva.2019.04.009
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    References listed on IDEAS

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    1. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
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    8. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    9. 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.
    10. Demongeot, Jacques & Hamie, Ali & Laksaci, Ali & Rachdi, Mustapha, 2016. "Relative-error prediction in nonparametric functional statistics: Theory and practice," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 261-268.
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    13. Germán Aneiros & Paula Raña & Philippe Vieu & Juan Vilar, 2018. "Bootstrap in semi-functional partial linear regression under dependence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(3), pages 659-679, September.
    14. 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.
    15. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
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    Cited by:

    1. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.
    2. Yousri Slaoui, 2021. "Recursive non-parametric kernel classification rule estimation for independent functional data," Computational Statistics, Springer, vol. 36(1), pages 79-112, March.
    3. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    4. Salim Bouzebda & Yousri Slaoui, 2023. "Nonparametric Recursive Estimation for Multivariate Derivative Functions by Stochastic Approximation Method," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 658-690, February.
    5. Yousri Slaoui, 2020. "Recursive nonparametric regression estimation for dependent strong mixing functional data," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 665-697, October.
    6. Slaoui Yousri & Khardani Salah, 2020. "Nonparametric relative recursive regression," Dependence Modeling, De Gruyter, vol. 8(1), pages 221-238, January.

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