A Nonparametric Multivariate Two-Sample Test Using Spanning Subgraphs

• Activity Number: 35
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): David Ruth*+
• Companies: U.S. Naval Academy
• Keywords: Combinatorial optimization ; Distribution-free test ; Non-parametric test ; Graph-theoretic procedure

Abstract

A new nonparametric test is proposed for the multivariate two-sample problem as an extension of Rosenbaum's Cross-Match Test (2005). The Cross-Match Test is distribution-free; this new test is asymptotically distribution-free but more powerful. Each observation is considered to be the vertex of a complete, undirected, weighted graph; interpoint distances are assigned as edge weights. A minimum-weight, r-regular spanning subgraph is constructed, where r is some number close to the size of the smaller sample. Like the Cross-Match Test (which is a special case of this test with r = 1), the proposed test statistic is the number of edges in the minimum-weight subgraph containing one observation from the first distribution and one from the second. Unequal distributions will tend to result in fewer edges that connect vertices between different groups. This test is sensitive to a wide range of distribution differences, including location and dispersion alternatives, and has noteworthy power characteristics. A simulation study includes a comparison of the performance of this new test with that of several competitors.