Multivariate-Sign-Based High-Dimensional Tests for the Two-Sample Location Problem

• 成果类型: Article
• 署名作者: Feng, Long; Zou, Changliang; Wang, Zhaojun
• 署名单位: Nankai University; Nankai University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2015.1035380
• 发表日期: 2016
• 页码: 721-735
• 关键词: Covariance matrices; REGRESSION-COEFFICIENTS; fewer observations; affine-invariant; mean vector; sample-size; microarray; dependence

摘要

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.