 |
Some Asymptotic Properties of the Conditional Set-Indexed Empirical Process Based on Dependent Functional Data
The purpose of this paper is to establish the invariance principle for the conditional
set-indexed empirical process formed by strong mixing random variables when the co-
variates are functional. We establish our results under some assumptions on the rich-
ness of the index class C of sets in terms of metric entropy with bracketing. We ap-
ply our main result for testing the conditional independence, that is, testing whether
whether two random vectors Y1 and Y2 are independent, given X. The theoretical re-
sults of the present paper are (or will be) key tools for many further developments in
functional data analysis.
