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Weak convergence of some randomly indexed empirical processes

Beghin L.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

333--342

In this paper, we shall be concerned with weak convergence of the randomly indexed versions of the standard and “independence” empirical processes, in the general framework of stochastic processes indexed by classes of functions and without any distributional assumption. We obtain, in the limit, some generalizations of well-known Gaussian fields such that those arising with a deterministic index are embedded as a special case.