Artículo
Henry, G.; Muñoz, A.; Rodriguez, D. "Locally adaptive density estimation on Riemannian manifolds" (2013) SORT. 37(2):111-130
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Abstract:
In this paper, we consider kernel type estimator with variable bandwidth when the random variables belong in a Riemannian manifolds. We study asymptotic properties such as the consistency and the asymptotic distribution. A simulation study is also considered to evaluate the performance of the proposal. Finally, to illustrate the potential applications of the proposed estimator, we analyse two real examples where two different manifolds are considered.
Registro:
| Documento: | Artículo |
| Título: | Locally adaptive density estimation on Riemannian manifolds |
| Autor: | Henry, G.; Muñoz, A.; Rodriguez, D. |
| Filiación: | Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Argentina CONICET, Argentina |
| Palabras clave: | Asymptotic results; Density estimation; Nonparametric; Riemannian manifolds; Asymptotic distributions; Asymptotic properties; Asymptotic results; Density estimation; Non-parametric; Riemannian manifold; Simulation studies; Variable bandwidths; Statistical methods; Statistics; Asymptotic analysis |
| Año: | 2013 |
| Volumen: | 37 |
| Número: | 2 |
| Página de inicio: | 111 |
| Página de fin: | 130 |
| Título revista: | SORT |
| Título revista abreviado: | SORT |
| ISSN: | 16962281 |
| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16962281_v37_n2_p111_Henry |
Referencias:
- Bai, Z.D., Rao, C., Zhao, L., Kernel estimators of density function of directional data (1988) Journal of Multivariate Analysis, 27, pp. 24-39
- Berger, M., Gauduchon, P., Mazet, E., (1971) Le Spectre d'Une Variété Riemannienne, , Springer-Verlag
- Boothby, W.M., (1975) An Introduction to Differentiable Manifolds and Riemannian Geometry, , Academic Press, New York
- Butler, R., (1992) Paleomagnetism:Magnetic Domains to Geologic Terranes, , Blackwell, Scientific Publications
- Cox, A., Doell, R., Review of paleomagnetism (1960) Geological Society of America Bulletin, 71, pp. 645-768
- Devroye, L., Wagner, T.J., The strong uniform consistency of nearest neighbor density estimates (1977) Annals of Statistics, 3, pp. 536-540
- Do Carmo, M., (1988) Geometria Riemaniana, , Proyecto Euclides IMPA. 2a edición
- Fisher, R.A., Dispersion on a sphere (1953) Proceedings of the Royal Society of London Ser. A, 217, pp. 295-305
- Fisher, N.I., Lewis, T., Embleton, B.J.J., (1987) Statistical Analysis of Spherical Data, , New York: Cambridge University Press
- Gallot, S., Hulin, D., Lafontaine, J., (2004) Riemannian Geometry, , Springer Third Edition
- Garćia-Portugués, E., Crujeiras, R., Gonzalez-Manteiga, W., (2011) Exploring Wind Direction and SO2 Concentration by Circular-linear Density Estimation, , Prepint
- Goh, A., Vidal, R., Unsupervised Riemannian clustering of probability density functions (2008) Lecture Notes in Artificial Intelligence, 5211
- Gray, A., Vanhecke, L., Riemannian geometry as determined by the volumes of small geodesic balls (1979) Acta Mathematica, 142, pp. 157-198
- Hall, P., Watson, G.S., Cabrera, J., Kernel density estimation with spherical data (1987) Biometrika, 74, pp. 751-762
- Henry, G., Rodriguez, D., Kernel density estimation on Riemannian manifolds: Asymptotic results (2009) Journal of Mathematical Imaging and Vision, 43, pp. 235-639
- Jammalamadaka, S., Sengupta, A., Topics in circular statistics (2001) Multivariate Analysis, 5. , World Scientific, Singapore
- Joshi, J., Srivastava, A., Jermyn, I.H., Riemannian analysis of probability density functions with applications in vision (2007) Proceedings of the IEEE Computer Vision and Pattern Recognition
- Love, J., Constable, C., Gaussian statistics for palaeomagnetic vectors (2003) Geophysical Journal International, 152, pp. 515-565
- Mardia, K., Jupp, P., (2000) Directional Data, , New York: Wiley
- Mardia, K., Sutton, T., A model for cylindrical variables with applications (1978) Journal of the Royal Statistical Society. Series B. (Methodological), 40, pp. 229-233
- Parzen, E., On estimation of a probability density function and mode (1962) The Annals of Mathematical Statistics, 33, pp. 1065-1076
- Pelletier, B., Kernel density estimation on Riemannian manifolds (2005) Statistics and Probability Letters, 73 (3), pp. 297-304
- Pennec, X., Intrinsic statistics on Riemannian manifolds: Basic tools for geometric measurements (2006) Journal of Mathematical Imaging and Vision, 25, pp. 127-154
- Rosenblatt, M., Remarks on some nonparametric estimates of a density function (1956) The Annals of Mathematical Statistics, 27, pp. 832-837
- Wagner, T., Nonparametric estimates of probability densities (1975) IEEE Transactions on Information Theory IT, 21, pp. 438-440
Citas:
---------- APA ----------
Henry, G., Muñoz, A. & Rodriguez, D. (2013) . Locally adaptive density estimation on Riemannian manifolds. SORT, 37(2), 111-130.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16962281_v37_n2_p111_Henry [ ]
---------- CHICAGO ----------
Henry, G., Muñoz, A., Rodriguez, D. "Locally adaptive density estimation on Riemannian manifolds" . SORT 37, no. 2 (2013) : 111-130.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16962281_v37_n2_p111_Henry [ ]
---------- MLA ----------
Henry, G., Muñoz, A., Rodriguez, D. "Locally adaptive density estimation on Riemannian manifolds" . SORT, vol. 37, no. 2, 2013, pp. 111-130.Recuperado de https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16962281_v37_n2_p111_Henry [ ]
---------- VANCOUVER ----------
Henry, G., Muñoz, A., Rodriguez, D. Locally adaptive density estimation on Riemannian manifolds. SORT. 2013;37(2):111-130.Available from: https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_16962281_v37_n2_p111_Henry [ ]
