Institute of Mathematical Statistics Lecture Notes - Monograph Series
- Lecture Notes--Monograph Series
- Volume 55, 2007, 234-252
Empirical processes indexed by estimated functions
Jon A. Wellner Wellner and Aad W. van der Vaart
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
Dates
First available in Project Euclid: 4 December 2007
Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196797079
Digital Object Identifier
doi:10.1214/074921707000000382
Mathematical Reviews number (MathSciNet)
MR2459942
Zentralblatt MATH identifier
1176.62050
Subjects
Primary: 62G07: Density estimation 62G08: Nonparametric regression 62G20: Asymptotic properties 62F05: Asymptotic properties of tests 62F15: Bayesian inference
Keywords
delta-method Donsker class entropy integral pseudo observation
Rights
Copyright © 2007, Institute of Mathematical Statistics
Citation
van der Vaart, Aad W.; Wellner, Jon A. Wellner. Empirical processes indexed by estimated functions. Asymptotics: Particles, Processes and Inverse Problems, 234--252, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000382. https://projecteuclid.org/euclid.lnms/1196797079
