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VOL. 51 | 2006 Stochastic integrals and asymptotic analysis of canonical von Mises statistics based on dependent observations
Igor S. Borisov, Alexander A. Bystrov

Editor(s) Evarist Giné, Vladimir Koltchinskii, Wenbo Li, Joel Zinn

## Abstract

In the first part of the paper we study stochastic integrals of a nonrandom function with respect to a nonorthogonal Hilbert noise defined on a semiring of subsets of an arbitrary nonempty set.

In the second part we apply this construction to study limit behavior of canonical (i.e., degenerate) Von Mises statistics based on weakly dependent stationary observations.

## Information

Published: 1 January 2006
First available in Project Euclid: 28 November 2007

zbMATH: 1123.60034
MathSciNet: MR2387757

Digital Object Identifier: 10.1214/074921706000000725

Subjects:
Primary: 60F05 , 60H05
Secondary: 62G20

Keywords: $\psi$-mixing , canonical $U$-statistics , canonical von Mises statistics , dependent observations , empirical process , nonorthogonal noise , stochastic integral