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
Rights: Copyright © 2006, Institute of Mathematical Statistics
