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October, 1995 Exponential Inequalities for Martingales, with Application to Maximum Likelihood Estimation for Counting Processes
Sara van de Geer
Ann. Statist. 23(5): 1779-1801 (October, 1995). DOI: 10.1214/aos/1176324323

Abstract

We obtain an exponential probability inequality for martingales and a uniform probability inequality for the process $\int g dN$, where $N$ is a counting process and where $g$ varies within a class of predictable functions $\mathscr{G}$. For the latter, we use techniques from empirical process theory. The uniform inequality is shown to hold under certain entropy conditions on $\mathscr{G}$. As an application, we consider rates of convergence for (nonparametric) maximum likelihood estimators for counting processes. A similar result for discrete time observations is also presented.

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Sara van de Geer. "Exponential Inequalities for Martingales, with Application to Maximum Likelihood Estimation for Counting Processes." Ann. Statist. 23 (5) 1779 - 1801, October, 1995. https://doi.org/10.1214/aos/1176324323

Information

Published: October, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0852.60019
MathSciNet: MR1370307
Digital Object Identifier: 10.1214/aos/1176324323

Subjects:
Primary: 60E15
Secondary: 62G05

Rights: Copyright © 1995 Institute of Mathematical Statistics

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Vol.23 • No. 5 • October, 1995
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