Change-point detection in high-dimensional covariance structure
By Valeriy Avanesov, Nazar Buzun. 2016
66 citations recorded by the source corpus.
In this paper we introduce a novel approach for an important problem of break detection. Specifically, we are interested in detection of an abrupt change in the covariance structure of a high-dimensional random process -- a problem, which has applications in many areas e.g., neuroimaging and finance. The developed approach is essentially a testing procedure involving a choice of a critical level. To that end a non-standard bootstrap scheme is proposed and theoretically justified under mild assumptions. Theoretical study features a result providing guaranties for break detection. All the theoretical results are established in a high-dimensional setting (dimensionality $p \gg n$). Multiscale nature of the approach allows for a trade-off between sensitivity of break detection and localization. The approach can be naturally employed in an on-line setting. Simulation study demonstrates that the approach matches the nominal level of false alarm probability and exhibits high power, outperforming a recent approach.
Subfields: Control and Systems Engineering, Finance, Statistics and Probability
View Paper: https://www.semanticscholar.org/paper/677fb0f69de20e480502ff2073fff52b64137508
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In Control and Systems Engineering
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Citations in the corpus
- Univariate mean change point detection: Penalization, CUSUM and optimality (2018, background): “…Cho and Fryzlewicz, 2015; Cho, 2015; Aston and Kirch, 2014; Jirak, 2015; Wang and Samworth, 2018), in covariance structures (e.g. Aue et al., 2009; Avanesov and Buzun, 2016; Wang et al., 2017), in dynamic networks (e.g. Gibberd and Roy, 2017; Wang et al., 2018), and in sequentially-correlated…”