Tail asymptotic behavior of the supremum of a class of chi-square processes
Ji, Lanpeng; Liu, Peng; Robert, Stephan
2019

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Abstract

We analyze in this paper the supremum of a class of chi-square processes over non-compact intervals, which can be seen as a multivariate counterpart of the generalized weighted Kolmogorov-Smirnov statistic. The boundedness and the exact tail asymptotic behavior of the supremum are derived. As examples, the chi-square process generated from the Brownian bridge and the fractional Brownian motion are discussed.

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Title Tail asymptotic behavior of the supremum of a class of chi-square processes
Author(s) Ji, Lanpeng (School of Mathematics, University of Leeds, Leeds, United Kingdom)
Liu, Peng (Department of Statistics and Actuarial Science, University of Waterloo, Canada)
Robert, Stephan (School of Engineering and Management Vaud, HES-SO, University of Applied Sciences and Arts Western Switzerland)
Date 2019-07
Published in Statistics Probability Letters
Volume 2019, vol. 154
Pagination 11 p.
DOI https://doi.org/10.1016/j.spl.2019.07.001
ISSN 0167-7152
Keywords chi-square process ; exact asymptotics ; brownian bridge
Article Type scientifique
Faculty Ingénierie et Architecture
School HEIG-VD
Institute IICT - Institut des Technologies de l'Information et de la Communication
Record Appears in Scientific Articles
Global
External resources Preprint on arXiv.org

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