Empirical processes indexed by estimated functions

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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.
Published at http://dx.doi.org/10.1214/074921707000000382 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org)

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Statistics Theory, 62G07, 62G08, 62G20, 62F05, 62F15 (Primary)

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http://salesiana.dossiersoluciones.com/handle/123456789/137701

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0709.1013
 http://arxiv.org/abs/0709.1013
 IMS Lecture Notes Monograph Series 2007, Vol. 55, 234-252
 doi:10.1214/074921707000000382

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arXiv