A Weighted Edge-Count Two-Sample Test for Multivariate and Object Data
提出一种基于相似图的非参数两样本检验方法，通过加权解决样本量不等问题，适用于多元和非欧几里得数据，在模拟和网络数据分析中表现良好。
Two-sample tests for multivariate data and non-Euclidean data are widely used in many fields. Parametric tests are mostly restrained to certain types of data that meets the assumptions of the parametric models. In this article, we study a nonparametric testing procedure that uses graphs representing the similarity among observations. It can be applied to any data types as long as an informative similarity measure on the sample space can be defined. The classic test based on a similarity graph has a problem when the two sample sizes are different. We solve the problem by applying appropriate weights to different components of the classic test statistic. The new test exhibits substantial power gains in simulation studies. Its asymptotic permutation null distribution is derived and shown to work well under finite samples, facilitating its application to large datasets. The new test is illustrated through an analysis on a real dataset of network data.