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Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data

Author

Listed:
  • Salim Bouzebda

    (Laboratoire de Mathématiques Appliquées de Compiègne (L.M.A.C.), Université de Technologie de Compiègne, 60200 Compiègne, France)

  • Youssouf Souddi

    (Laboratory of Stochastic Models, Statistics and Applications, University of Saida-Dr. Moulay Tahar, P.O. Box 138 EN-NASR, Saïda 20000, Algeria)

  • Fethi Madani

    (Laboratory of Stochastic Models, Statistics and Applications, University of Saida-Dr. Moulay Tahar, P.O. Box 138 EN-NASR, Saïda 20000, Algeria)

Abstract

This work examines the asymptotic characteristics of a conditional set-indexed empirical process composed of functional ergodic random variables with missing at random (MAR). This paper’s findings enlarge the previous advancements in functional data analysis through the use of empirical process methodologies. These results are shown under specific structural hypotheses regarding entropy and under appealing situations regarding the model. The regression operator’s asymptotic ( 1 − α ) -confidence interval is provided for 0 < α < 1 as an application. Additionally, we offer a classification example to demonstrate the practical importance of the methodology.

Suggested Citation

  • Salim Bouzebda & Youssouf Souddi & Fethi Madani, 2024. "Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data," Mathematics, MDPI, vol. 12(3), pages 1-22, January.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:3:p:448-:d:1329886
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    References listed on IDEAS

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    Cited by:

    1. Fatimah A. Almulhim & Mohammed B. Alamari & Mustapha Rachdi & Ali Laksaci, 2024. "Recursive Estimation of the Expectile-Based Shortfall in Functional Ergodic Time Series," Mathematics, MDPI, vol. 12(24), pages 1-17, December.

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