  One of the major problems for maximum likelihood estimation in the
well-established directional models is that the normalising constants can be
difficult to evaluate. A new general method of "score matching estimation" is
presented here on a compact oriented Riemannian manifold. Important
applications include von Mises-Fisher, Bingham and joint models on the sphere
and related spaces. The estimator is consistent and asymptotically normally
distributed under mild regularity conditions. Further, it is easy to compute as
a solution of a linear set of equations and requires no knowledge of the
normalizing constant. Several examples are given, both analytic and numerical,
to demonstrate its good performance.
