Nonparametric likelihood based estimation for a multivariate Lipschitz density |
| |
Authors: | Daniel Carando |
| |
Institution: | a Departamento de Matemática, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Pabellón 1, Ciudad Universitaria, 1428 Buenos Aires, Argentina b Departamento de Matemática, Universidad de San Andrés, Vito Dumas 284 (1644), Victoria, Pcia. de Buenos Aires, Argentina |
| |
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. |
| |
Keywords: | primary 62G07 secondary 62F30 62G20 |
本文献已被 ScienceDirect 等数据库收录! |
|