  Sphericity test plays a key role in many statistical problems. We propose
Spearman's rho-type rank test and Kendall's tau-type rank test for sphericity
in the high dimensional settings. We show that these two tests are equivalent.
Thanks to the "blessing of dimension", we do not need to estimate any nuisance
parameters. Without estimating the location parameter, we can allow the
dimension to be arbitrary large. Asymptotic normality of these two tests are
also established under elliptical distributions. Simulations demonstrate that
they are very robust and efficient in a wide range of settings.
