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

Hao Chen and Yin Xia

Journal of the American Statistical Association, 2023, vol. 118, issue 541, 719-731

Abstract: 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.

Date: 2023
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DOI: 10.1080/01621459.2021.1953507

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