Some Characteristics of the Conditional Set-Indexed Empirical Process Involving Functional Ergodic Data
Résumé
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.