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...
Guardado en:
| Autores principales: | , |
|---|---|
| Publicado: |
2009
|
| Materias: | |
| 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: |
| Sumario: | 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. |
|---|