Nonparametric likelihood based estimation for a multivariate Lipschitz density

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., Bos...

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Detalles Bibliográficos
Autores principales:	Carando, Daniel German, Groisman, Pablo Jose
Publicado:	2009
Materias:	62F30 62G07 62G20 Density estimation Maximum likelihood primary secondary Tailor-made estimates
Acceso en línea:	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v100_n5_p981_Carando http://hdl.handle.net/20.500.12110/paper_0047259X_v100_n5_p981_Carando
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	paper:paper_0047259X_v100_n5_p981_Carando
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spelling	paper:paper_0047259X_v100_n5_p981_Carando2023-06-08T15:05:34Z Nonparametric likelihood based estimation for a multivariate Lipschitz density Carando, Daniel German Groisman, Pablo Jose 62F30 62G07 62G20 Density estimation Maximum likelihood primary secondary Tailor-made estimates 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. Fil:Carando, D. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Fil:Groisman, P. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2009 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v100_n5_p981_Carando http://hdl.handle.net/20.500.12110/paper_0047259X_v100_n5_p981_Carando
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	62F30 62G07 62G20 Density estimation Maximum likelihood primary secondary Tailor-made estimates
spellingShingle	62F30 62G07 62G20 Density estimation Maximum likelihood primary secondary Tailor-made estimates Carando, Daniel German Groisman, Pablo Jose Nonparametric likelihood based estimation for a multivariate Lipschitz density
topic_facet	62F30 62G07 62G20 Density estimation Maximum likelihood primary secondary Tailor-made estimates
description	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.
author	Carando, Daniel German Groisman, Pablo Jose
author_facet	Carando, Daniel German Groisman, Pablo Jose
author_sort	Carando, Daniel German
title	Nonparametric likelihood based estimation for a multivariate Lipschitz density
title_short	Nonparametric likelihood based estimation for a multivariate Lipschitz density
title_full	Nonparametric likelihood based estimation for a multivariate Lipschitz density
title_fullStr	Nonparametric likelihood based estimation for a multivariate Lipschitz density
title_full_unstemmed	Nonparametric likelihood based estimation for a multivariate Lipschitz density
title_sort	nonparametric likelihood based estimation for a multivariate lipschitz density
publishDate	2009
url	https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_0047259X_v100_n5_p981_Carando http://hdl.handle.net/20.500.12110/paper_0047259X_v100_n5_p981_Carando
work_keys_str_mv	AT carandodanielgerman nonparametriclikelihoodbasedestimationforamultivariatelipschitzdensity AT groismanpablojose nonparametriclikelihoodbasedestimationforamultivariatelipschitzdensity
_version_	1768542880424525824

Nonparametric likelihood based estimation for a multivariate Lipschitz density

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