Open Access
December 2014 Limit theorems for nondegenerate U-statistics of continuous semimartingales
Mark Podolskij, Christian Schmidt, Johanna F. Ziegel
Ann. Appl. Probab. 24(6): 2491-2526 (December 2014). DOI: 10.1214/13-AAP983


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.


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Mark Podolskij. Christian Schmidt. Johanna F. Ziegel. "Limit theorems for nondegenerate U-statistics of continuous semimartingales." Ann. Appl. Probab. 24 (6) 2491 - 2526, December 2014.


Published: December 2014
First available in Project Euclid: 26 August 2014

zbMATH: 1308.60051
MathSciNet: MR3262509
Digital Object Identifier: 10.1214/13-AAP983

Primary: 60F05 , 60F15 , 60F17
Secondary: 60G48 , 60H05

Keywords: $U$-statistics , High frequency data , limit theorems , Semimartingales , stable convergence

Rights: Copyright © 2014 Institute of Mathematical Statistics

Vol.24 • No. 6 • December 2014
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