The Annals of Applied Probability

Limit theorems for nondegenerate U-statistics of continuous semimartingales

Mark Podolskij, Christian Schmidt, and Johanna F. Ziegel

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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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Ann. Appl. Probab., Volume 24, Number 6 (2014), 2491-2526.

First available in Project Euclid: 26 August 2014

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Zentralblatt MATH identifier

Primary: 60F05: Central limit and other weak theorems 60F15: Strong theorems 60F17: Functional limit theorems; invariance principles
Secondary: 60G48: Generalizations of martingales 60H05: Stochastic integrals

High frequency data limit theorems semimartingales stable convergence $U$-statistics


Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F. Limit theorems for nondegenerate U -statistics of continuous semimartingales. Ann. Appl. Probab. 24 (2014), no. 6, 2491--2526. doi:10.1214/13-AAP983.

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