On a projection-based class of uniformity tests on the hypersphere

We introduce a projection-based class of uniformity tests on the hypersphere. The employs statistics that integrate, along all possible directions, weighted quadratic discrepancy between empirical cumulative distribution projections and projected uniform distribution. Simple expressions for several test are obtained circle sphere, as well relatively tractable forms higher dimensions. Despite their different origins, variants proposed shown to contain be contained in Sobolev tests. Our new proves itself advantageous by allowing derivation neatly extend circular-only Watson, Ajne, Rothman, introducing first instance an Anderson–Darling-like directional data. obtain usable asymptotic distributions local optimality against certain alternatives A simulation study evaluates theoretical findings provides evidence testing proposals competitive. An application crater Rhea illustrates usage