Podolskij, Mark; Schmidt, Christian; Ziegel, Johanna F. (2014). Limit theorems for nondegenerate U-statistics of continuous semimartingales. Annals of applied probability, 24(6), pp. 2491-2526. Institute of Mathematical Statistics 10.1214/13-AAP983
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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.
Item Type: |
Journal Article (Original Article) |
|---|---|
Division/Institute: |
08 Faculty of Science > Department of Mathematics and Statistics > Institute of Mathematical Statistics and Actuarial Science |
UniBE Contributor: |
Ziegel, Johanna F. |
Subjects: |
300 Social sciences, sociology & anthropology > 360 Social problems & social services 500 Science > 510 Mathematics |
ISSN: |
1050-5164 |
Publisher: |
Institute of Mathematical Statistics |
Language: |
English |
Submitter: |
Lutz Dümbgen |
Date Deposited: |
06 Oct 2014 13:20 |
Last Modified: |
05 Dec 2022 14:37 |
Publisher DOI: |
10.1214/13-AAP983 |
BORIS DOI: |
10.7892/boris.58539 |
URI: |
https://boris.unibe.ch/id/eprint/58539 |
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