Electronic Journal of Statistics

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

Davit Varron

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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

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

First available in Project Euclid: 3 November 2014

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Empirical processes random measures Bayesian nonparametrics


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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