A Normality Test for High-dimensional Data Based on the Nearest Neighbor Approach

• 成果类型: Article
• 署名作者: Chen, Hao; Xia, Yin
• 署名单位: University of California System; University of California Davis; Fudan University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2021.1953507
• 发表日期: 2023
• 页码: 719-731
• 关键词: 2-sample test; multivariate normality; selection; CLASSIFICATION; MODEL

摘要

Many statistical methodologies for high-dimensional data assume the population is normal. Although a few multivariate normality tests have been proposed, to the best of our knowledge, none of them can properly control the Type I error when the dimension is larger than the number of observations. In this work, we propose a novel nonparametric test that uses the nearest neighbor information. The proposed method guarantees the asymptotic Type I error control under the high-dimensional setting. Simulation studies verify the empirical size performance of the proposed test when the dimension grows with the sample size and at the same time exhibit a superior power performance of the new test compared with alternative methods. We also illustrate our approach through two popularly used datasets in high-dimensional classification and clustering literatures where deviation from the normality assumption may lead to invalid conclusions.