  We use Stein characterizations to obtain new moment-type estimators for the
parameters of three classical spherical distributions (namely the
Fisher-Bingham, the von Mises-Fisher, and the Watson distributions) in the
i.i.d. case. This leads to explicit estimators which have good asymptotic
properties (close to efficiency) and therefore lead to interesting alternatives
to classical maximum likelihood methods or more recent score matching
estimators. We perform competitive simulation studies to assess the quality of
the new estimators. Finally, the practical relevance of our estimators is
illustrated on a real data application in spherical latent representations of
handwritten numbers.
