On weighted sign tests for rotational symmetry on hyperspheres

Abstract

Rotational symmetry is a classical assumption when inference for directional data has to be performed. In the present paper, we study a class of weighted sign procedures for testing the (null) hypothesis of rotational symmetry around a fixed axis. Particular instances of the tests we study are locally and asymptotically optimal tests against the skewed alternatives considered in Ley and Verdebout (J Multivariate Anal 159:67–81 2017 [10]) and the tangent von Mises alternatives considered in García-Portugués et al. (J Amer Statist Assoc 115:1873–1887 2020 [3]). Monte Carlo simulations confirm our theoretical results.