## The Annals of Statistics

### $U$-Processes: Rates of Convergence

#### 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.

#### Article information

Source
Ann. Statist. Volume 15, Number 2 (1987), 780-799.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176350374

JSTOR
Nolan, Deborah; Pollard, David. $U$-Processes: Rates of Convergence. The Annals of Statistics 15 (1987), no. 2, 780--799. doi:10.1214/aos/1176350374. http://projecteuclid.org/euclid.aos/1176350374.