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

Salim Bouzebda (), Youssouf Souddi and Fethi Madani
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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

Mathematics, 2024, vol. 12, issue 3, 1-22

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.

Keywords: conditional distribution; small ball probability; missing at random; empirical process; ergodic functional data; semi-metric space; covering number (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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