A Basic Result on the Consistency of Maximum Likelihood Estimators
A sequence fXig of independent and identically distributed random objects is considered. The common distribution of the X i's is absolutely continuous with respect to a givenmeasure, and the corresponding density is not completely speciØed but depends on an unknown parameter. Under mild topolog...
| Autor: | |
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| Tipo de recurso: | informe técnico |
| Estado: | Versión publicada |
| Fecha de publicación: | 2007 |
| País: | México |
| Institución: | Centro de Investigación en Matemáticas |
| Repositorio: | Repositorio Institucional CIMAT |
| Idioma: | inglés |
| OAI Identifier: | oai:cimat.repositorioinstitucional.mx:1008/637 |
| Acceso en línea: | http://cimat.repositorioinstitucional.mx/jspui/handle/1008/637 |
| Access Level: | acceso abierto |
| Palabra clave: | info:eu-repo/classification/MSC/Estimación info:eu-repo/classification/cti/1 info:eu-repo/classification/cti/12 info:eu-repo/classification/cti/1209 info:eu-repo/classification/cti/120909 |
| Sumario: | A sequence fXig of independent and identically distributed random objects is considered. The common distribution of the X i's is absolutely continuous with respect to a givenmeasure, and the corresponding density is not completely speciØed but depends on an unknown parameter. Under mild topological and continuity requirements, a necessary and su±cient crite- rion for the consistency of a sequence of maximum likelihood estimators is obtained. When this characterization is applied to the case in which the parameter belongs to a Ønite dimensional Euclidean space, the conclusion is that the sequence is consistent if and only if it is bounded with probability .1. |
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