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Estimating the Conditional Density in Scalar-On-Function Regression Structure: k -N-N Local Linear Approach

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)

  • Zoulikha Kaid

    (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

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

Abstract

In this study, the problem of conditional density estimation of a scalar response variable, given a functional covariable, is considered. A new estimator is proposed by combining the k -nearest neighbors ( k -N-N) procedure with the local linear approach. Then, the uniform consistency in the number of neighbors (UNN) of the proposed estimator is established. Such result is useful in the study of some data-driven rules. As a direct application and consequence of the conditional density estimation, we derive the UNN consistency of the conditional mode function estimator. Finally, to highlight the efficiency and superiority of the obtained results, we applied our new estimator to real data and compare it to its existing competitive estimator.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:6:p:902-:d:769112
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    References listed on IDEAS

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    Cited by:

    1. Sultana DIDI & Ahoud AL HARBY & Salim BOUZEBDA, 2022. "Wavelet Density and Regression Estimators for Functional Stationary and Ergodic Data: Discrete Time," Mathematics, MDPI, vol. 10(19), pages 1-33, September.

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