Limit theorems for nondegenerate U-statistics of continuous semimartingales
Probability
2014-09-10 v2 Statistics Theory
Statistics Theory
Abstract
This paper presents the asymptotic theory for nondegenerate -statistics of high frequency observations of continuous It\^{o} semimartingales. We prove uniform convergence in probability and show a functional stable central limit theorem for the standardized version of the -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.
Keywords
Cite
@article{arxiv.1210.0358,
title = {Limit theorems for nondegenerate U-statistics of continuous semimartingales},
author = {Mark Podolskij and Christian Schmidt and Johanna F. Ziegel},
journal= {arXiv preprint arXiv:1210.0358},
year = {2014}
}
Comments
Published in at http://dx.doi.org/10.1214/13-AAP983 the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)