  Compositional data and multivariate count data with known totals are
challenging to analyse due to the non-negativity and sum-to-one constraints on
the sample space. It is often the case that many of the compositional
components are highly right-skewed, with large numbers of zeros. A major
limitation of currently available estimators for compositional models is that
they either cannot handle many zeros in the data or are not computationally
feasible in moderate to high dimensions. We derive a new set of novel score
matching estimators applicable to distributions on a Riemannian manifold with
boundary, of which the standard simplex is a special case. The score matching
method is applied to estimate the parameters in a new flexible truncation model
for compositional data and we show that the estimators are scalable and
available in closed form. Through extensive simulation studies, the scoring
methodology is demonstrated to work well for estimating the parameters in the
new truncation model and also for the Dirichlet distribution. We apply the new
model and estimators to real microbiome compositional data and show that the
model provides a good fit to the data.
