Estimating a Change Point in a Sequence of Very High-Dimensional Covariance Matrices. Issue 537 (2nd January 2022)

• Record Type: Journal Article
• Authors: Dette, Holger; Pan, Guangming; Yang, Qing
• Is Part Of: Journal of the American Statistical Association. Volume 117:Issue 537(2022)
• Page Start: 444
• Page End: 454
• Publication Date: 2022-01-02
• Subjects: Change point analysis -- Dimension reduction -- High-dimensional covariance matrices; Statistics -- Periodicals; Statistics -- Periodicals; Statistiques -- Périodiques; États-Unis -- Statistiques -- Périodiques; 519.5
• DOI: 10.1080/01621459.2020.1785477
• Languages: English
• ISSNs: 0162-1459

Abstract

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.