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.

摘要

本文考虑在一个高维向量序列中估计协方差矩阵中的一个变化点的问题，其中维数远大于样本量。提出了一种两阶段的方法来有效地估计变化点的位置。第一步包括减少维度以识别对应于显着变化的协方差矩阵的元素。第二步，我们使用降维后的组件来确定变化点的位置。为这两个步骤开发了理论特性，并进行了数值研究以支持新方法。本文的补充材料可在线获取。