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

Holger Dette, Guangming Pan, Qing Yang

2020Journal of the American Statistical Association24 citationsDOI

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.

Topics & Concepts

CovarianceDimension (graph theory)Sequence (biology)Covariance matrixPoint (geometry)MathematicsPosition (finance)Matrix (chemical analysis)Reduction (mathematics)Estimation of covariance matricesDimensionality reductionApplied mathematicsStatisticsAlgorithmComputer scienceCombinatoricsGeometryArtificial intelligenceEconomicsBiologyComposite materialFinanceGeneticsMaterials scienceStatistical Methods and InferenceAdvanced Statistical Methods and ModelsSensory Analysis and Statistical Methods