## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### Empirical processes indexed by estimated functions

#### Abstract

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. We recast their examples in terms of empirical process theory, and provide an alternative general view which should be of wide applicability.

#### Chapter information

Source
Eric A. Cator, Geurt Jongbloed, Cor Kraaikamp, Hendrik P. Lopuhaä, Jon A. Wellner, eds., Asymptotics: Particles, Processes and Inverse Problems: Festschrift for Piet Groeneboom (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 234-252

Dates
First available in Project Euclid: 4 December 2007

https://projecteuclid.org/euclid.lnms/1196797079

Digital Object Identifier
doi:10.1214/074921707000000382

Mathematical Reviews number (MathSciNet)
MR2459942

Zentralblatt MATH identifier
1176.62050

Rights