Limit theorems for nondegenerate U-statistics of continuous semimartingales

DOI
Publisher DOI
Abstract
This paper presents the asymptotic theory for nondegenerate U-statistics of high frequency observations of continuous Itô semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the U-statistic. The limiting process in the central limit theorem turns out to be conditionally Gaussian with mean zero. Finally, we indicate potential statistical applications of our probabilistic results.
Date Issued
2014-12-01
Publication Type
Article
Subject(s)
Language(s)
en
Author(s)
Podolskij, Mark
Schmidt, Christian
Additional Credits
Journal
Annals of applied probability
Publisher
Institute of Mathematical Statistics
ISSN
1050-5164
Access(Rights)
restricted
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