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Estimating a Change Point in a Sequence of Very High-Dimensional Covariance Matrices

Dette, H. and Pan, G. and Yang, Q.

JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
Volume: Pages:
DOI: 10.1080/01621459.2020.1785477
Published: 2020

Abstract
This article considers the problem of estimating a change point in the covariance matrix in a sequence of high-dimensional vectors, where the dimension is substantially larger than the sample size. A two-stage approach is proposed to efficiently estimate the location of the change point. The first step consists of a reduction of the dimension to identify elements of the covariance matrices corresponding to significant changes. In a second step, we use the components after dimension reduction to determine the position of the change point. Theoretical properties are developed for both steps, and numerical studies are conducted to support the new methodology. Supplementary materials for this article are available online. © 2020 American Statistical Association.

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