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Abstract:

The paper concerns the strong uniform consistency and the asymptotic distribution of the kernel density estimator of random objects on a Riemannian manifolds, proposed by Pelletier (Stat. Probab. Lett., 73(3):297-304, 2005). The estimator is illustrated via one example based on a real data. © 2009 Springer Science+Business Media, LLC.

Registro:

Documento: Artículo
Título:Kernel density estimation on Riemannian manifolds: Asymptotic results
Autor:Henry, G.; Rodriguez, D.
Filiación:Departamento de Matemática, FCEyN, Ciudad Universitaria, Pabellón I, C1428EHA Buenos Aires, Argentina
Palabras clave:Geometry; Nonparametric estimation; Riemannian manifolds; Statistics; Asymptotic distributions; Example based; Kernel Density Estimation; Kernel density estimators; Nonparametric estimation; Riemannian manifold; Riemannian manifolds; Asymptotic analysis; Distribution functions; Statistical tests; Estimation
Año:2009
Volumen:34
Número:3
Página de inicio:235
Página de fin:239
DOI: http://dx.doi.org/10.1007/s10851-009-0145-2
Título revista:Journal of Mathematical Imaging and Vision
Título revista abreviado:J Math Imaging Vision
ISSN:09249907
CODEN:JMIVE
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_09249907_v34_n3_p235_Henry

Referencias:

  • Bai, Z.D., Rao, C., Zhao, L., Kernel estimators of density function of directional data (1988) J. Multivar. Anal., 27, pp. 24-39
  • Berger, M., Gauduchon, P., Mazet, E., (1971) Le Spectre d'∈Une Variété Riemannienne, , Springer Berlin
  • Besse, A., (1978) Manifolds All of Whose Geodesics Are Closed, , Springer Berlin
  • Bhattacharya, R., Patrangenaru, V., Nonparametric estimation of location and dispersion on Riemannian manifolds (2002) J. Stat. Plan. Inference, 108, pp. 23-35
  • Boothby, W.M., (1975) An Introduction to Differentiable Manifolds and Riemannian Geometry, , Academic Press New York
  • Do Carmo, M., Geometria Riemaniana, Proyecto Euclides, 2dn edn (1988) IMPA
  • Fisher, N.I., Lewis, T., Embleton, B.J.J., (1987) Statistical Analysis of Spherical Data, , Cambridge University Press New York
  • Goh, A., Vidal, R., Unsupervised Riemannian clustering of probability density functions (2008) Lecture Notes in Artificial Intelligence, 5211
  • Hall, P., Watson, G.S., Cabrera, J., Kernel density estimation with spherical data (1987) Biometrika, 74, pp. 751-762
  • Hendriks, H., Landsman, Z., Asymptotic data analysis on manifolds (2007) Ann. Stat., 35 (1), pp. 109-131
  • Henry, G., Rodriguez, D., Robust nonparametric regression on Riemannian manifolds (2009) J. Nonparametr. Stat, , to appear
  • Joshi, J., Srivastava, A., Jermyn, I.H., Riemannian analysis of probability density functions with applications in vision (2007) Proc. IEEE Computer Vision and Pattern Recognition
  • Mardia, K., (1972) Statistics of Directional Data, , Academic Press London
  • Pelletier, B., Kernel density estimation on Riemannian manifolds (2005) Statistics and Probability Letters, 73 (3), pp. 297-304. , DOI 10.1016/j.spl.2005.04.004, PII S0167715205001239
  • Pelletier, B., Nonparametric regression estimation on closed Riemannian manifolds (2006) J. Nonparametr. Stat., 18, pp. 57-67
  • Pennec, X., Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements (2006) Journal of Mathematical Imaging and Vision, 25 (1), pp. 127-154. , DOI 10.1007/s10851-006-6228-4

Citas:

---------- APA ----------
Henry, G. & Rodriguez, D. (2009) . Kernel density estimation on Riemannian manifolds: Asymptotic results. Journal of Mathematical Imaging and Vision, 34(3), 235-239.
http://dx.doi.org/10.1007/s10851-009-0145-2
---------- CHICAGO ----------
Henry, G., Rodriguez, D. "Kernel density estimation on Riemannian manifolds: Asymptotic results" . Journal of Mathematical Imaging and Vision 34, no. 3 (2009) : 235-239.
http://dx.doi.org/10.1007/s10851-009-0145-2
---------- MLA ----------
Henry, G., Rodriguez, D. "Kernel density estimation on Riemannian manifolds: Asymptotic results" . Journal of Mathematical Imaging and Vision, vol. 34, no. 3, 2009, pp. 235-239.
http://dx.doi.org/10.1007/s10851-009-0145-2
---------- VANCOUVER ----------
Henry, G., Rodriguez, D. Kernel density estimation on Riemannian manifolds: Asymptotic results. J Math Imaging Vision. 2009;34(3):235-239.
http://dx.doi.org/10.1007/s10851-009-0145-2