High-dimensional rank tests for sphericity

In recent years, procedures for testing distributional sphericity have attracted increased attention, especially in high-dimensional settings. A prominent problem in this context is the development of robust and efficient test statistics. In this paper, we propose two novel rank tests inspired by Spearman's rho and Kendall's tau for high-dimensional problems. Due to the “blessing of dimension”, estimation of masses of nuisance parameters is avoided, which allows our procedures to work in arbitrary large dimension. The asymptotic normality of the proposed tests is established for elliptical distributions and their performance is investigated over a wide range of simulation set-ups.