标题： 由估计函数索引的经验过程 显示英文标题

标题： Empirical processes indexed by estimated functions

摘要： 我们研究了以依赖于估计参数的函数为索引的经验过程的收敛性，并给出了若干替代条件，在这些条件下，"估计参数"$\eta$可以在其自然极限$\eta_n$上被均匀替换为另一个索引集$\eta_0$上的$\Theta$。 特别是，我们重新审视了Ghoudi和Remillard [Asymptotic Methods in Probability and Statistics (1998) 171--197, Fields Inst. Commun. 44 (2004) 381--406]处理的一些例子。我们将他们的例子重新表述为经验过程理论的形式，并提供了一个替代性的通用视角，这应该具有广泛的应用性。 显示英文摘要

摘要： We consider the convergence of empirical processes indexed by functions that depend on an estimated parameter $\eta$ and give several alternative conditions under which the ``estimated parameter'' $\eta_n$ can be replaced by its natural limit $\eta_0$ uniformly in some other indexing set $\Theta$. 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.