“Ensemble Subsampling for Imbalanced Multivariate Two-Sample Tests,”
针对两样本量不平衡时多元分布相等性检验功效下降的问题，提出一种基于最近邻法和集成子采样的新检验方法，推导了渐近分布并证明一致性，模拟和公司金融实例显示其功效随样本量比增大而提高。
Chang and Ye Luo for helpful discussions. Their sincere gratitude also goes to three anonymous reviewers, an AE and the co-editor Xuming He for many constructive comments and suggestions. Some existing nonparametric two-sample tests for equality of multivariate distributions perform unsatisfactorily when the two sample sizes are unbalanced. In particular, the power of these tests tends to diminish with increasingly unbalanced sample sizes. In this paper, we propose a new testing procedure to solve this problem. The proposed test, based on a nearest neighbor method by Schilling (1986a), employs a novel ensemble subsampling scheme to remedy this issue. More specifically, the test statistic is a weighted average of a collection of statistics, each associated with a randomly selected subsample of the data. We derive the asymptotic distribution of the test statistic under the null hypothesis and show that the new test is consistent against all alternatives when the ratio of the sample sizes either goes to a finite limit or tends to infinity. Via simulated data examples we demonstrate that the new test has increasing power with increasing sample size ratio when the size of the smaller sample is fixed. The test is applied to a real data example in the field of Corporate Finance.