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Asymptotic Results of Some Conditional Nonparametric Functional Parameters in High-Dimensional Associated Data

Author

Listed:
  • Hamza Daoudi

    (Department of Electrical Engineering, College of Technology, Tahri Mohamed University, Bechar 08000, Algeria)

  • Zouaoui Chikr Elmezouar

    (Department of Mathematics, College of Science, King Khalid University, Abha 61413, Saudi Arabia)

  • Fatimah Alshahrani

    (Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, Riyadh 11671, Saudi Arabia)

Abstract

In this paper, we propose to study the asymptotic properties of some conditional functional parameters, such as the distribution function, the density, and the hazard function, for an explanatory variable with values in a Hilbert space (infinite dimension) and a response variable real in a quasi-associated dependency framework. We consider the non parametric estimation of the conditional distribution function by the kernel method in the presence of the quasi-associated dependence, and we establish under general hypotheses the almost complete convergence with speed of the estimator built in the associated case. The estimation of the conditional hazard function will be conducted by utilizing the two outcomes of the conditional distribution function and the conditional density. We establish the asymptotic normality of the kernel estimator as the conditional risk function of a properly normalized functional. We explicitly give the asymptotic variance. Simulation studies were conducted to investigate the behavior of the asymptotic property in the context of finite sample data. All the statistical analyses were performed using R software.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:20:p:4290-:d:1259917
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    References listed on IDEAS

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    4. Bulinski, Alexander & Suquet, Charles, 2001. "Normal approximation for quasi-associated random fields," Statistics & Probability Letters, Elsevier, vol. 54(2), pages 215-226, September.
    5. Daoudi Hamza & Boubaker Mechab & Chikr Elmezouar Zouaoui, 2020. "Asymptotic normality of a conditional hazard function estimate in the single index for quasi-associated data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 49(3), pages 513-530, February.
    6. Matula, Przemyslaw, 1992. "A note on the almost sure convergence of sums of negatively dependent random variables," Statistics & Probability Letters, Elsevier, vol. 15(3), pages 209-213, October.
    7. 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.
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