Abstract

In this paper, we propose a new homogeneous test for two highdimensional random vectors. Our test is built on a new measure, the so-called

characteristic distance, which can completely characterize the homogeneity of

two distributions. The newly proposed metric has some desirable properties, for

example, it possesses a clear and intuitive probabilistic interpretation, and can

be used to address the high-dimensional distance inference. Theoretically, the

limiting behaviors under the conventional fixed dimension and high-dimensional

distance inference are thoroughly investigated. Simulation studies and real data

analysis are presented to illustrate the finite-sample performance of the proposed

test statistic.

Key words and phrases: Characteristic distance, High Dimensionality, Test of Homogeneity, U-statistic, Permutation procedure

Information

Preprint No.SS-2023-0299
Manuscript IDSS-2023-0299
Complete AuthorsXu Li, Gongming Shi, Baoxue Zhang
Corresponding AuthorsBaoxue Zhang
Emailszhangbaoxue@cueb.edu.cn

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Acknowledgments

Zhang’s work is supported by the National Natural Science Foundation of

China (12271370). Li’s work is supported by the National Natural Science

Foundation of China (12401356), and the Natural Science Foundation of

Shanxi Province, China (202203021222223, 20210302124262, 20210302124531).

Supplementary Materials

Additional supporting materials can be found in the Supplementary Materials, including proof of the theoretical results presented in Sections 2-4, as

well as some additional simulation results.

Supplementary materials are available for download.