B0977
Title: A general maximal projection approach to uniformity testing on the hypersphere
Authors: Bruno Ebner - Karlsruhe Institute of Technology (Germany) [presenting]
Jaroslav Borodavka - Karlsruhe Institute of Technology (Germany)
Abstract: A novel approach is proposed to uniformity testing on the d-dimensional unit hypersphere based on maximal projections. This approach gives a unifying view on the classical uniformity tests of Rayleigh and Bingham, as well as links to measures of multivariate skewness and kurtosis. The limiting distribution is derived under the null hypothesis using limit theorems for Banach space-valued stochastic processes and present strategies to simulate the limiting processes by applying results on spherical harmonics theory. The behavior under contiguous and fixed alternatives is examined and consistency of the testing procedure is shown for some classes of alternatives. Bahadur efficiency statements are included for some alternatives. The theoretical findings and empirical powers of the procedures are evaluated in a broad competitive Monte Carlo simulation study.
