Nonparametric curve estimation on Stiefel manifolds

Jeffrey M. Lee, Frits H. Ruymgaart

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The main result is a speed of a.s. uniform convergence for estimators of nonparametric regression functions on Stiefel manifolds. The Stiefel 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 part 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.

Original languageEnglish
Pages (from-to)57-68
Number of pages12
JournalJournal of Nonparametric Statistics
Issue number1
StatePublished - 1996


  • Compound empirical process
  • Nonparametric regression
  • Stiefel manifold
  • Uniform convergence


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