  We propose a general and relatively simple method for the construction of
goodness-of-fit tests on the sphere and the hypersphere. The method is based on
the characterization of probability distributions via their characteristic
function, and it leads to test criteria that are convenient regarding
applications and consistent against arbitrary deviations from the model under
test. We emphasize goodness-of-fit tests for spherical distributions due to
their importance in applications and the relative scarcity of available
methods.
