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June, 1987 $U$-Processes: Rates of Convergence
Deborah Nolan, David Pollard
Ann. Statist. 15(2): 780-799 (June, 1987). DOI: 10.1214/aos/1176350374

Abstract

This paper introduces a new stochastic process, a collection of $U$-statistics indexed by a family of symmetric kernels. Conditions are found for the uniform almost-sure convergence of a sequence of such processes. Rates of convergence are obtained. An application to cross-validation in density estimation is given. The proofs adapt methods from the theory of empirical processes.

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Deborah Nolan. David Pollard. "$U$-Processes: Rates of Convergence." Ann. Statist. 15 (2) 780 - 799, June, 1987. https://doi.org/10.1214/aos/1176350374

Information

Published: June, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0624.60048
MathSciNet: MR888439
Digital Object Identifier: 10.1214/aos/1176350374

Subjects:
Primary: 60F15
Secondary: 60G20, 62G99

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 2 • June, 1987
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