Limit theorems for nondegenerate U-statistics of continuous semimartingales
This paper presents the asymptotic theory for nondegenerate UUU-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 UUU-statistic. The limiting...
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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
26 August 2014
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| In: |
The annals of applied probability
Year: 2014, Volume: 24, Issue: 6, Pages: 2491-2526 |
| ISSN: | 2168-8737 |
| DOI: | 10.1214/13-AAP983 |
| Online Access: | Verlag, Volltext: http://dx.doi.org/10.1214/13-AAP983 Verlag, Volltext: http://projecteuclid.org/euclid.aoap/1409058038 
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| Author Notes: | Mark Podolskij, Christian Schmidt and Johanna F. Ziegel |
MARC
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| 520 | |a This paper presents the asymptotic theory for nondegenerate UUU-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 UUU-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. | ||
| 650 | 4 | |a $U$-statistics | |
| 650 | 4 | |a High frequency data | |
| 650 | 4 | |a limit theorems | |
| 650 | 4 | |a semimartingales | |
| 650 | 4 | |a stable convergence | |
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