On a modified Watson test for spherical location

Abstract

In this work, we study a modified Watson test for the one sample spherical location problem. Our test is based on a modification of the classical Watson test. As is well-known, the Watson test is asymptotically valid under rotational symmetry and locally and asymptotically optimal in the von Mises case. We show that our modified Watson test enjoys several nice features: (i) it remains asymptotically valid under a large class of distributions including the rotational symmetric ones and (ii) it enjoys some local and asymptotic optimality properties in the vicinity of the von Mises case. Our results are supported by Monte Carlo simulations.