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 demonstrate its competitive performance.

Key words and phrases: Change point inference; High dimensions; Linear regres- sion; Multiplier bootstrap; Subgroups

Information

Preprint No.SS-2023-0212
Manuscript IDSS-2023-0212
Complete AuthorsBin Liu, Xinsheng Zhang, Yufeng Liu
Corresponding AuthorsYufeng Liu
Emailsyfliu@email.unc.edu

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Acknowledgments

The authors would like to thank the editor, the associate editor, and

the reviewers for their helpful comments and suggestions.

Supplementary Materials

The online supplementary materials provide detailed basic assumptions

and proofs of the main theory, and additional numerical results including

size, power, multiple change point detection. In addition, an interesting

real data application is also provided.

Supplementary materials are available for download.