Nonparametric curve estimation on stiefel manifolds
Jeffrey M. Lee, Frits H. Ruymgaart · Journal of nonparametric statistics · 1996
The main result is a speed of a.s. uniform convergence for estimators of nonparametric regression Junctions on Stiefel manifolds. The Sticfcl manifold is not only of interest in its own right but also because it generalizes both the sphere and the orthogonal group. The main tool for the variance pari is a local fluctuation inequality for the compound empirical process indexed by simple subsets of the manifold that we call caps. For the bias part the symmetry of the Stiefel manifold is exploited. It turns out that this symmetry is sufficient to obtain the same overall rate as in a Euclidean space of the same dimension.