IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v9y2021i10p1102-d553873.html
   My bibliography  Save this article

Smooth k NN Local Linear Estimation of the Conditional Distribution Function

Author

Listed:
  • Ibrahim M. Almanjahie

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
    Statistical Research and Studies Support Unit, King Khalid University, Abha 62529, Saudi Arabia)

  • Zouaoui Chikr Elmezouar

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
    Statistical Research and Studies Support Unit, King Khalid University, Abha 62529, Saudi Arabia)

  • Ali Laksaci

    (Department of Mathematics, College of Science, King Khalid University, Abha 62529, Saudi Arabia
    Statistical Research and Studies Support Unit, King Khalid University, Abha 62529, Saudi Arabia)

  • Mustapha Rachdi

    (AGIM Team, Laboratoire AGEIS, EA 7407, Université Grenoble Alpes (France), UFR SHS, BP. 47, CEDEX 09, F38040 Grenoble, France)

Abstract

Previous works were dedicated to the functional k -Nearest Neighbors ( k NN) and the local linearity method estimations of a regression operator. In this paper, a sequence pair of ( X i , Y i ) i = 1 , … , n of functional mixing observations are considered. We treat the local linear estimation of the cumulative function of Y i given functional input variable X i . Precisely, we combine the k NN method with the local linear algorithm to construct a new and fast efficiency estimator of the conditional distribution function. The main purpose of this paper is to prove the strong convergence of the constructed estimator under mixing conditions. An application to the functional times series prediction is used to compare our proposed estimator with the existing competitive estimators, and show its efficiency and superiority.

Suggested Citation

  • Ibrahim M. Almanjahie & Zouaoui Chikr Elmezouar & Ali Laksaci & Mustapha Rachdi, 2021. "Smooth k NN Local Linear Estimation of the Conditional Distribution Function," Mathematics, MDPI, vol. 9(10), pages 1-14, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1102-:d:553873
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/9/10/1102/pdf
    Download Restriction: no
    File URL: https://www.mdpi.com/2227-7390/9/10/1102/
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Zouaoui Chikr-Elmezouar & Ibrahim M. Almanjahie & Ali Laksaci & Mustapha Rachdi, 2019. "FDA: strong consistency of the NN local linear estimation of the functional conditional density and mode," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 31(1), pages 175-195, January.
    2. Kudraszow, Nadia L. & Vieu, Philippe, 2013. "Uniform consistency of kNN regressors for functional variables," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1863-1870.
    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. Yao, Qiwei & Tong, Howell, 1995. "On initial-condition sensitivity and prediction in nonlinear stochastic systems," LSE Research Online Documents on Economics 6402, London School of Economics and Political Science, LSE Library.
    5. 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.
    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. 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.
    8. 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.
    9. Gooijer, Jan G. De & Gannoun, Ali, 2000. "Nonparametric conditional predictive regions for time series," Computational Statistics & Data Analysis, Elsevier, vol. 33(3), pages 259-275, May.
    10. A. Berlinet & A. Elamine & A. Mas, 2011. "Local linear regression for functional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(5), pages 1047-1075, October.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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. Litimein, Ouahiba & Laksaci, Ali & Mechab, Boubaker & Bouzebda, Salim, 2023. "Local linear estimate of the functional expectile regression," Statistics & Probability Letters, Elsevier, vol. 192(C).
    3. 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.
    4. 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.
    5. Chagny, Gaëlle & Roche, Angelina, 2016. "Adaptive estimation in the functional nonparametric regression model," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 105-118.
    6. Ibrahim M. Almanjahie & Zoulikha Kaid & Ali Laksaci & Mustapha Rachdi, 2022. "Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach," Mathematics, MDPI, vol. 10(6), pages 1-16, March.
    7. Saâdia Rahmani & Oussama Bouanani, 2023. "Local linear estimation of the conditional cumulative distribution function: Censored functional data case," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 85(1), pages 741-769, February.
    8. 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.
    9. 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.
    10. Abderrahmane Belguerna & Hamza Daoudi & Khadidja Abdelhak & Boubaker Mechab & Zouaoui Chikr Elmezouar & Fatimah Alshahrani, 2024. "A Comprehensive Analysis of MSE in Estimating Conditional Hazard Functions: A Local Linear, Single Index Approach for MAR Scenarios," Mathematics, MDPI, vol. 12(3), pages 1-20, February.
    11. 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.
    12. 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.
    13. 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.
    14. Litimein, Ouahiba & Laksaci, Ali & Ait-Hennani, Larbi & Mechab, Boubaker & Rachdi, Mustapha, 2024. "Asymptotic normality of the local linear estimator of the functional expectile regression," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    15. Bouabsa Wahiba, 2022. "Unform in Bandwith of the Conditional Distribution Function with Functional Explanatory Variable: The Case of Spatial Data with the K Nearest Neighbour Method," Econometrics. Advances in Applied Data Analysis, Sciendo, vol. 26(2), pages 30-46, June.
    16. 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.
    17. Elías, Antonio & Jiménez, Raúl & Shang, Han Lin, 2022. "On projection methods for functional time series forecasting," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    18. 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.
    19. Alexander Gleim & Nazarii Salish, 2022. "Forecasting Environmental Data: An example to ground-level ozone concentration surfaces," Papers 2202.03332, arXiv.org.
    20. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:9:y:2021:i:10:p:1102-:d:553873. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.