Asymptotic normality of interpoint distances for high-dimensional data with applications to the two-sample problem

• 成果类型: Article
• 署名作者: Li, Jun
• 署名单位: University of California System; University of California Riverside
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/asy020
• 发表日期: 2018
• 页码: 529546
• 关键词: geometric representation; mild conditions; MULTIVARIATE; tests

摘要

Interpoint distances have applications in many areas of probability and statistics. Thanks to their simplicity of computation, interpoint distance-based procedures are particularly appealing for analysing small samples of high-dimensional data. In this paper, we first study the asymptotic distribution of interpoint distances in the high-dimension, low-sample-size setting and show that it is normal under regularity conditions. We then construct a powerful test for the two-sample problem, which is consistent for detecting location and scale differences. Simulations show that the test compares favourably with existing distance-based tests.