  Given an m-dimensional compact submanifold $\mathbf{M}$ of Euclidean space
$\mathbf{R}^s$, the concept of mean location of a distribution, related to mean
or expected vector, is generalized to more general $\mathbf{R}^s$-valued
functionals including median location, which is derived from the spatial
median. The asymptotic statistical inference for general functionals of
distributions on such submanifolds is elaborated. Convergence properties are
studied in relation to the behavior of the underlying distributions with
respect to the cutlocus. An application is given in the context of independent,
but not identically distributed, samples, in particular, to a multisample
setup.
