Empirical processes indexed by estimated functions

@inproceedings{Vaart2007EmpiricalPI,
  title={Empirical processes indexed by estimated functions},
  author={Aad van der Vaart and J. A. Wellner},
  year={2007}
}
We consider the convergence of empirical processes indexed by functions that depend on an estimated parameter η and give several alternative conditions under which the “estimated parameter” ηn can be replaced by its natural limit η0 uniformly in some other indexing set Θ. In particular we reconsider some examples treated by Ghoudi and Remillard [Asymptotic Methods in Probability and Statistics (1998) 171–197, Fields Inst. Commun. 44 (2004) 381–406]. We recast their examples in terms of… CONTINUE READING

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