  When observations are truncated, we are limited to an incomplete picture of
our dataset. Recent methods propose to use score matching for truncated density
estimation, where the access to the intractable normalising constant is not
required. We present a novel extension of truncated score matching to a
Riemannian manifold with boundary. Applications are presented for the von
Mises-Fisher and Kent distributions on a two dimensional sphere in
$\mathbb{R}^3$, as well as a real-world application of extreme storm
observations in the USA. In simulated data experiments, our score matching
estimator is able to approximate the true parameter values with a low
estimation error and shows improvements over a naive maximum likelihood
estimator.
