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

2018/07/27 by Holger Dette, Dette, H., Guangming Pan +3
Mathematics · #Advanced Statistical Methods and Models #FOS: Computer and information sciences #FOS: Mathematics #Methodology (stat.ME) #Statistical Methods and Inference #Statistical and numerical algorithms #Statistics Theory (math.ST)

paper · pdf · doi:10.48550/arxiv.1807.10797

openalex publication_date 2018/07/27 · openalex created_date 2018/08/03 · openalex updated_date 2026/07/28

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.

Citations

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