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Preprint (Author's original)arXiv.org - Non-exclusive license to distribute, Open
Preprint
Change point detection in high dimensional data with U-statistics
arXiv (Cornell University)
18 Jul 2022
Abstract
We consider the problem of detecting distributional changes in a sequence of
high dimensional data. Our approach combines two separate statistics stemming
from $L_p$ norms whose behavior is similar under $H_0$ but potentially
different under $H_A$, leading to a testing procedure that that is flexible
against a variety of alternatives. We establish the asymptotic distribution of
our proposed test statistics separately in cases of weakly dependent and
strongly dependent coordinates as $\min\{N,d\}\to\infty$, where $N$ denotes
sample size and $d$ is the dimension, and establish consistency of testing and
estimation procedures in high dimensions under one-change alternative settings.
Computational studies in single and multiple change point scenarios demonstrate
our method can outperform other nonparametric approaches in the literature for
certain alternatives in high dimensions. We illustrate our approach though an
application to Twitter data concerning the mentions of U.S. Governors.
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Details
- Title
- Change point detection in high dimensional data with U-statistics
- Creators
- B. Cooper BonieceLajos HorváthPeter Jacobs
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861653404721