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Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data

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  • Rachdi, Mustapha
  • Laksaci, Ali
  • Demongeot, Jacques
  • Abdali, Abdel
  • Madani, Fethi

Abstract

The problem of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space is considered. Some theoretical and practical asymptotic properties of this estimator are established. The usefulness of the estimator is highlighted through the exact expression involved in the leading terms of the quadratic error, and by conducting a computational investigation to show the superiority of this estimation method for the conditional density and then for the conditional mode. Moreover, in order to verify the pertinence of the technique, from a practical point of view, it is applied to a real dataset.

Suggested Citation

  • Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    • Handle: RePEc:eee:csdana:v:73:y:2014:i:c:p:53-68
    DOI: 10.1016/j.csda.2013.11.011
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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. Eduardo L. Montoya & Wendy Meiring, 2016. "An F-type test for detecting departure from monotonicity in a functional linear model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(2), pages 322-337, June.
    3. Bouabsa Wahiba, 2023. "The Estimating of the Conditional Density with Application to the Mode Function in Scalar-On-Function Regression Structure: Local Linear Approach with Missing at Random," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 27(1), pages 17-32, March.
    4. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    5. Somia Ayad & Ali Laksaci & Saâdia Rahmani & Rachida Rouane, 2020. "On the local linear modelization of the conditional density for functional and ergodic data," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 237-254, August.
    6. 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.
    7. Xiong, Xianzhu & Ou, Meijuan & Chen, Ailian, 2021. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model," Statistics & Probability Letters, Elsevier, vol. 168(C).
    8. Benhenni, Karim & Hassan, Ali Hajj & Su, Yingcai, 2019. "Local polynomial estimation of regression operators from functional data with correlated errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 80-94.
    9. 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.
    10. Demongeot, Jacques & Naceri, Amina & Laksaci, Ali & Rachdi, Mustapha, 2017. "Local linear regression modelization when all variables are curves," Statistics & Probability Letters, Elsevier, vol. 121(C), pages 37-44.
    11. 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.
    12. Oussama Bouanani & Saâdia Rahmani & Ali Laksaci & Mustapha Rachdi, 2020. "Asymptotic normality of conditional mode estimation for functional dependent data," Indian Journal of Pure and Applied Mathematics, Springer, vol. 51(2), pages 465-481, June.
    13. Chaouch, Mohamed, 2019. "Volatility estimation in a nonlinear heteroscedastic functional regression model with martingale difference errors," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 129-148.
    14. Mustapha Rachdi & Ali Laksaci & Zoulikha Kaid & Abbassia Benchiha & Fahimah A. Al‐Awadhi, 2021. "k‐Nearest neighbors local linear regression for functional and missing data at random," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 42-65, February.
    15. Karim Benhenni & Sonia Hedli-Griche & Mustapha Rachdi, 2017. "Regression models with correlated errors based on functional random design," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(1), pages 1-21, March.
    16. Boukhiar, Souad & Mourid, Tahar, 2022. "Resolvent estimators for functional autoregressive processes with random coefficients," Journal of Multivariate Analysis, Elsevier, vol. 189(C).

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