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arXiv · 0709.1013

Empirical processes indexed by estimated functions

Aad W. van der Vaart·Jon A. Wellner
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Abstract

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'' $η_n$ can be replaced by its natural limit $η_0$ 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 empirical process theory, and provide an alternative general view which should be of wide applicability.

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Aad W. van der Vaart, Jon A. Wellner. 2007-09-07. Empirical processes indexed by estimated functions. https://doi.org/10.1214/074921707000000382

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