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Local polynomial modelling of the conditional quantile for functional data

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  • Fatiha Messaci
  • Nahima Nemouchi
  • Idir Ouassou
  • Mustapha Rachdi

Abstract

As the problem of prediction is of great interest, several tools based on different methods and devoted to various contexts, have been developed in the statistical literature. The contribution of this paper is to focus on the study of the local linear nonparametric estimation of the quantile of a scalar response variable given a functional covariate. In fact, the covariate is a random variable taking values in a semi-metric space which can have an infinite dimension in order to permit to deal with curves. We first establish pointwise and uniform almost-complete convergences, with rates, of the conditional distribution function estimator. Then, we deduce the uniform almost-complete convergence of the obtained local linear conditional quantile estimator. We also bring out the application of our results to the multivariate case as well as to the particular case of the kernel method. Moreover, a real data study allows to place our conditional median estimator in relation to several other predictive tools. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • Fatiha Messaci & Nahima Nemouchi & Idir Ouassou & Mustapha Rachdi, 2015. "Local polynomial modelling of the conditional quantile for functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 24(4), pages 597-622, November.
    • Handle: RePEc:spr:stmapp:v:24:y:2015:i:4:p:597-622
    DOI: 10.1007/s10260-015-0296-9
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    References listed on IDEAS

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    1. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    2. K. Benhenni & F. Ferraty & M. Rachdi & P. Vieu, 2007. "Local smoothing regression with functional data," Computational Statistics, Springer, vol. 22(3), pages 353-369, September.
    3. J. Barrientos-Marin & F. Ferraty & P. Vieu, 2010. "Locally modelled regression and functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(5), pages 617-632.
    4. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.
    5. Frédéric Ferraty & Ali Laksaci & Philippe Vieu, 2006. "Estimating Some Characteristics of the Conditional Distribution in Nonparametric Functional Models," Statistical Inference for Stochastic Processes, Springer, vol. 9(1), pages 47-76, May.
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    Cited by:

    1. Fahimah A. Al-Awadhi & Zoulikha Kaid & Ali Laksaci & Idir Ouassou & Mustapha Rachdi, 2019. "Functional data analysis: local linear estimation of the $$L_1$$ L 1 -conditional quantiles," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 217-240, June.
    2. Zhiyong Zhou & Zhengyan Lin, 2016. "Asymptotic normality of locally modelled regression estimator for functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(1), pages 116-131, March.
    3. Lihong Wang, 2020. "Nearest neighbors estimation for long memory functional data," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 29(4), pages 709-725, December.
    4. Ali Laksaci & Elias Ould Saïd & Mustapha Rachdi, 2021. "Uniform consistency in number of neighbors of the kNN estimator of the conditional quantile model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(6), pages 895-911, August.

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