On the multivariate runs test

• 成果类型: Article
• 署名作者: Henze, N; Penrose, MD
• 署名单位: Helmholtz Association; Karlsruhe Institute of Technology; Durham University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 1999
• 页码: 290-298
• 关键词: minimal spanning tree; nearest neighbor; 2-sample tests; probability; statistics; number

摘要

For independent d-variate random variables X-1,...,X-m with common density f and Y-1,...; Y-n with common density g, let R-m,R-n be the number of edges in the minimal spanning tree with vertices X-1,..., X-m, Y-1,...,Y-n that connect points from different samples. Friedman and Rafsky conjectured that a test of H-o: f = g that rejects H-o for small values of R-m,R-n should have power against general alternatives. We prove that R-m,R-n is asymptotically distribution-free under H-o, and that the multivariate two-sample test based on R-m,R-n is universally consistent.