Strong uniform convergence of density estimators on compact Euclidean manifolds

Abstract

In this note the naive estimators for densities on the sphere in Ruymgaart (1989) are generalised to compact smooth submanifolds of a Euclidean space and their convergence behaviour is studied. As special examples are treated Stiefel manifolds (which include both the sphere and the orthogonal groups). Furthermore in the last section some goodness of fit procedures are discussed.Density estimation goodness of fit Stiefel manifold Grasman manifold Euclidean manifolds