Given an m-dimensional compact submanifold M of Euclidean space Rs, the concept of mean location of a distribution, related to mean or expected vector, is generalized to more general Rs-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.
"Asymptotic data analysis on manifolds." Ann. Statist. 35 (1) 109 - 131, February 2007. https://doi.org/10.1214/009053606000000993