Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data
by Youssouf Souddi   Fethi Madani   Salim Bouzebda  

Vol. 16 No. 4 (2021) P.367~P.399

DOI:	https://doi.org/10.21915/BIMAS.2021405
	10.21915/BIMAS.2021405

ABSTRACT

The purpose of this paper is to establish the invariance principle for the conditional set-indexed empirical process formed by functional ergodic random variables. The limit theorems, discussed in this paper, are key tools for many further developments in functional data analysis involving empirical process techniques. These results are proved under some standard structural conditions on the Vapnik-Chervonenkis classes of functions and some mild conditions on the model.

KEYWORDS
Conditional distribution, Nadaraya-Watson regression estimator, Empirical process, Ergodic, Functional data, Semi-metric space, Covering number, Small ball probability

MATHEMATICAL SUBJECT CLASSIFICATION 2010
Primary: 62G20, 62G10, 62M15

MILESTONES

Received: 2021-12-02
Revised :
Accepted: 2021-12-21

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