Limit theorems for nondegenerate U-statistics of continuous semimartingales

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:

25 Apr 2017 23:47

Publisher DOI:

10.1214/13-AAP983

BORIS DOI:

10.7892/boris.58539

URI:

https://boris.unibe.ch/id/eprint/58539

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