Two-sample spatial rank test using projection

ABSTRACT

This paper explores in high-dimensional settings how to test the equality of two location vectors. We introduce a rank-based projection test under elliptical symmetry. Optimal projection direction is derived according to asymptotically and locally best power criteria. Data-splitting strategy is used to estimate optimal projection and construct test statistics. The limiting null distribution and power function of the proposed statistics are thoroughly investigated under some mild assumptions. The test is shown to keep type I error rates pretty well and outperforms several existing methods in a broad range of settings, especially in the presence of large correlation structures. Simulation studies are conducted to confirm the asymptotic results and a real data example is applied to demonstrate the advantage of the proposed procedure.

KEYWORDS:

• High-dimensional mean test problem
• locally optimal test
• nonparametric test
• sample splitting
• spatial rank test

Acknowledgements

The authors thank the editor, the associate editor, and an anonymous referee for many helpful comments that have resulted in significant improvements in the article.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported by NNSF of China grant nos. [11690015, 11622104, 11431006, 11771332 and 11371202].