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

Salim Bouzebda (1) , Youssouf Souddi , Fethi Madani

1 LMAC - Laboratoire de Mathématiques Appliquées de Compiègne

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.

Domaines: Théorie [stat.TH]; Analyse fonctionnelle [math.FA]; Probabilités [math.PR]

Salim Bouzebda, Youssouf Souddi, Fethi Madani. Weak Convergence of the Conditional Set-Indexed Empirical Process for Missing at Random Functional Ergodic Data. Mathematics , 2024, 12 (3), pp.448. ⟨10.3390/math12030448⟩. ⟨hal-04427506⟩