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Strong uniform convergence of density estimators on compact Euclidean manifolds

Author

Listed:
  • Hendriks, H.
  • Janssen, J. H. M.
  • Ruymgaart, F. H.

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.

Suggested Citation

  • Hendriks, H. & Janssen, J. H. M. & Ruymgaart, F. H., 1993. "Strong uniform convergence of density estimators on compact Euclidean manifolds," Statistics & Probability Letters, Elsevier, vol. 16(4), pages 305-311, March.
    • Handle: RePEc:eee:stapro:v:16:y:1993:i:4:p:305-311
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    Citations

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    Cited by:

    1. Klemelä, Jussi, 2000. "Estimation of Densities and Derivatives of Densities with Directional Data," Journal of Multivariate Analysis, Elsevier, vol. 73(1), pages 18-40, April.
    2. Loubes Jean-Michel & Pelletier Bruno, 2008. "A kernel-based classifier on a Riemannian manifold," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 35-51, March.
    3. Guillermo Henry & Daniela Rodriguez, 2009. "Robust nonparametric regression on Riemannian manifolds," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 21(5), pages 611-628.
    4. Pelletier, Bruno, 2005. "Kernel density estimation on Riemannian manifolds," Statistics & Probability Letters, Elsevier, vol. 73(3), pages 297-304, July.

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