Abstract:
We consider a problem of nonparametric density estimation under shape restrictions. We deal with the case where the density belongs to a class of Lipschitz functions. Devroye [L. Devroye, A Course in Density Estimation, in: Progress in Probability and Statistics, vol. 14, Birkhäuser Boston Inc., Boston, MA, 1987] considered these classes of estimates as tailor-made estimates, in contrast in some way to universally consistent estimates. In our framework we get the existence and uniqueness of the maximum likelihood estimate as well as strong consistency. This NPMLE can be easily characterized but it is not easy to compute. Some simpler approximations are also considered. © 2008 Elsevier Inc. All rights reserved.
Registro:
| Documento: |
Artículo
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| Título: | Nonparametric likelihood based estimation for a multivariate Lipschitz density |
| Autor: | Carando, D.; Fraiman, R.; Groisman, P. |
| Filiación: | Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellon 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina
Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284, 1644 Victoria, Pcia. de Buenos Aires, Argentina
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| Palabras clave: | 62F30; 62G07; 62G20; Density estimation; Maximum likelihood; primary; secondary; Tailor-made estimates |
| Año: | 2009
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| Volumen: | 100
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| Número: | 5
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| Página de inicio: | 981
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| Página de fin: | 992
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| DOI: |
http://dx.doi.org/10.1016/j.jmva.2008.10.001 |
| Título revista: | Journal of Multivariate Analysis
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| Título revista abreviado: | J. Multivariate Anal.
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| ISSN: | 0047259X
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| CODEN: | JMVAA
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| Registro: | https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v100_n5_p981_Carando |
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Citas:
---------- APA ----------
Carando, D., Fraiman, R. & Groisman, P.
(2009)
. Nonparametric likelihood based estimation for a multivariate Lipschitz density. Journal of Multivariate Analysis, 100(5), 981-992.
http://dx.doi.org/10.1016/j.jmva.2008.10.001---------- CHICAGO ----------
Carando, D., Fraiman, R., Groisman, P.
"Nonparametric likelihood based estimation for a multivariate Lipschitz density"
. Journal of Multivariate Analysis 100, no. 5
(2009) : 981-992.
http://dx.doi.org/10.1016/j.jmva.2008.10.001---------- MLA ----------
Carando, D., Fraiman, R., Groisman, P.
"Nonparametric likelihood based estimation for a multivariate Lipschitz density"
. Journal of Multivariate Analysis, vol. 100, no. 5, 2009, pp. 981-992.
http://dx.doi.org/10.1016/j.jmva.2008.10.001---------- VANCOUVER ----------
Carando, D., Fraiman, R., Groisman, P. Nonparametric likelihood based estimation for a multivariate Lipschitz density. J. Multivariate Anal. 2009;100(5):981-992.
http://dx.doi.org/10.1016/j.jmva.2008.10.001
