Asymptotic distribution-free change-point detection based on interpoint distances for high-dimensional data

Abstract

Recent advances have greatly facilitated the collection of high-dimensional data in many fields. Often the dimension of the data is much larger than the sample size, the so-called high dimension, low sample size setting. One important research problem is how to develop efficient change-point detection procedures for this new setting. Thanks to their simplicity of computation, interpoint distance-based procedures provide a potential solution to this problem. However, most of the existing distance-based procedures fail to fully utilise interpoint distances, and as a result, they suffer significant loss of power. In this paper, we propose a new asymptotic distribution-free distance-based change-point detection procedure for the high dimension, low sample size setting. The proposed procedure is proven to be consistent for detecting both location and scale changes and can also provide a consistent estimator for the change-point. Our simulation study and real data analysis show that it significantly outperforms the existing methods across a variety of settings.

Keywords:

• Bayesian-type statistic
• change-point
• high-dimensional data
• interpoint distance
• scan-type statistic

AMS Subject Classifications:

• 62G10
• 62G20

Acknowledgments

The author thanks the Editor, the Associate Editor and three anonymous referees for their constructive comments and suggestions, which greatly improved the quality of the paper.

Disclosure statement

No potential conflict of interest was reported by the author.