Asymptotic distribution-free change-point detection based on interpoint distances for high-dimensional data. Issue 1 (2nd January 2020)

• Record Type: Journal Article
• Authors: Li, Jun
• Is Part Of: Journal of nonparametric statistics. Volume 32:Issue 1(2020)
• Page Start: 157
• Page End: 184
• Publication Date: 2020-01-02
• Subjects: Bayesian-type statistic -- change-point -- high-dimensional data -- interpoint distance -- scan-type statistic; 62G10 -- 62G20; Nonparametric statistics -- Periodicals; 519.5
• DOI: 10.1080/10485252.2019.1710505
• Languages: English
• ISSNs: 1048-5252

Abstract

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.