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B0294
Title: Testing for spherical location in the vicinity of the uniform distribution Authors:  Davy Paindaveine - Universite libre de Bruxelles (Belgium) [presenting]
Thomas Verdebout - Universite Libre de Bruxelles (Belgium)
Abstract: The problem of testing the null hypothesis that the location parameter of a rotationally symmetric distribution is equal to a given value is considered. Motivated by a real-data example that shows little deviation from uniformity on the sphere, we investigate the robustness of the Watson test and of the Wald test based on the spherical mean under a sequence of null hypotheses that are contiguous to the uniform. We show that, while these classical tests are asymptotically equivalent away from uniformity, they exhibit very different behaviours in the vicinity of uniformity. Our asymptotic investigation also extends to non-null sequences of hypotheses. The finite-sample relevance of our theoretical results is illustrated through Monte Carlo simulations.