Simultaneous Change Point Detection and Identification for High Dimensional Linear Models

TL;DR

This paper introduces a new method for detecting and identifying change points in high-dimensional linear models, effectively controlling error rates and accurately locating change points, with applications demonstrated on Alzheimer's data.

Contribution

The paper proposes novel testing and estimation procedures for change point detection and identification in high-dimensional linear models, extending to multiple change points with binary segmentation.

Findings

Method controls type I error asymptotically

Achieves power against sparse alternatives

Demonstrates effectiveness on Alzheimer's disease data

Abstract

In this article, we consider change point inference for high dimensional linear models. For change point detection, given any subgroup of variables, we propose a new method for testing the homogeneity of corresponding regression coefficients across the observations. Under some regularity conditions, the proposed new testing procedure controls the type I error asymptotically and is powerful against sparse alternatives and enjoys certain optimality. For change point identification, an argmax based change point estimator is proposed which is shown to be consistent for the true change point location. Moreover, combining with the binary segmentation technique, we further extend our new method for detecting and identifying multiple change points. Extensive numerical studies justify the validity of our new method and an application to the Alzheimer's disease data analysis further demonstrate its competitive performance.