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Uniform in bandwidth consistency for various kernel estimators involving functional data

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Listed:
  • Lydia Kara-Zaitri
  • Ali Laksaci
  • Mustapha Rachdi
  • Philippe Vieu

Abstract

The paper investigates various nonparametric models including regression, conditional distribution, conditional density and conditional hazard function, when the covariates are infinite dimensional. The main contribution is to prove uniform in bandwidth asymptotic results for kernel estimators of these functional operators. Then, the application issues, involving data-driven bandwidth selection, are discussed.

Suggested Citation

  • Lydia Kara-Zaitri & Ali Laksaci & Mustapha Rachdi & Philippe Vieu, 2017. "Uniform in bandwidth consistency for various kernel estimators involving functional data," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 29(1), pages 85-107, January.
    • Handle: RePEc:taf:gnstxx:v:29:y:2017:i:1:p:85-107
    DOI: 10.1080/10485252.2016.1254780
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    References listed on IDEAS

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    1. Masry, Elias, 2005. "Nonparametric regression estimation for dependent functional data: asymptotic normality," Stochastic Processes and their Applications, Elsevier, vol. 115(1), pages 155-177, January.
    2. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    3. 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.
    4. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    5. Alejandro Quintela-Del-Río, 2008. "Hazard function given a functional variable: Non-parametric estimation under strong mixing conditions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 20(5), pages 413-430.
    6. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    7. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    8. Heng Lian, 2011. "Functional partial linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 115-128.
    9. Mariano Valderrama, 2007. "An overview to modelling functional data," Computational Statistics, Springer, vol. 22(3), pages 331-334, September.
    10. Aneiros, Germán & Vieu, Philippe, 2014. "Variable selection in infinite-dimensional problems," Statistics & Probability Letters, Elsevier, vol. 94(C), pages 12-20.
    11. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    12. Ouadah, Sarah, 2013. "Uniform-in-bandwidth nearest-neighbor density estimation," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1835-1843.
    13. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    14. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
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    Citations

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    Cited by:

    1. Belarbi, Faiza & Chemikh, Souheyla & Laksaci, Ali, 2018. "Local linear estimate of the nonparametric robust regression in functional data," Statistics & Probability Letters, Elsevier, vol. 134(C), pages 128-133.
    2. Salim Bouzebda & Amel Nezzal & Tarek Zari, 2022. "Uniform Consistency for Functional Conditional U -Statistics Using Delta-Sequences," Mathematics, MDPI, vol. 11(1), pages 1-39, December.
    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. 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.
    5. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    6. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    7. Hamza Daoudi & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2023. "Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data," Mathematics, MDPI, vol. 11(20), pages 1-24, October.
    8. Salim Bouzebda & Inass Soukarieh, 2022. "Non-Parametric Conditional U -Processes for Locally Stationary Functional Random Fields under Stochastic Sampling Design," Mathematics, MDPI, vol. 11(1), pages 1-69, December.
    9. Sudaraka Tholkage & Qi Zheng & Karunarathna B. Kulasekera, 2022. "Conditional Kaplan–Meier Estimator with Functional Covariates for Time-to-Event Data," Stats, MDPI, vol. 5(4), pages 1-17, November.
    10. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    11. Salim Bouzebda & Boutheina Nemouchi, 2023. "Weak-convergence of empirical conditional processes and conditional U-processes involving functional mixing data," Statistical Inference for Stochastic Processes, Springer, vol. 26(1), pages 33-88, April.

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