Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem
针对数据维度大于样本量的两样本位置检验问题，提出一种基于留一法的多元符号检验，能有效控制第一类错误，且对分量尺度差异具有不变性。
This article concerns tests for the two-sample location problem when data dimension is larger than the sample size. Existing multivariate-sign-based procedures are not robust against high dimensionality, producing tests with Type I error rates far away from nominal levels. This is mainly due to the biases from estimating location parameters. We propose a novel test to overcome this issue by using the “leave-one-out” idea. The proposed test statistic is scalar-invariant and thus is particularly useful when different components have different scales in high-dimensional data. Asymptotic properties of the test statistic are studied. Compared with other existing approaches, simulation studies show that the proposed method behaves well in terms of sizes and power. Supplementary materials for this article are available online.