Electronic Journal of Statistics

Donsker and Glivenko-Cantelli theorems for a class of processes generalizing the empirical process

Davit Varron

Full-text: Open access

Abstract

We establish a Glivenko-Cantelli and a Donsker theorem for a class of random discrete measures which generalize the empirical measure, under conditions on uniform entropy numbers that are common in empirical processes theory. Some illustrative applications in nonparametric Bayesian theory and randomly sized sampling are provided.

Article information

Source
Electron. J. Statist., Volume 8, Number 2 (2014), 2296-2320.

Dates
First available in Project Euclid: 3 November 2014

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1415023526

Digital Object Identifier
doi:10.1214/14-EJS955

Mathematical Reviews number (MathSciNet)
MR3275745

Zentralblatt MATH identifier
1320.60092

Subjects
Primary: 60F17: Functional limit theorems; invariance principles 60G57: Random measures 62F15: Bayesian inference

Keywords
Empirical processes random measures Bayesian nonparametrics

Citation

Varron, Davit. Donsker and Glivenko-Cantelli theorems for a class of processes generalizing the empirical process. Electron. J. Statist. 8 (2014), no. 2, 2296--2320. doi:10.1214/14-EJS955. https://projecteuclid.org/euclid.ejs/1415023526


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