Quasi-concave density estimation
| Autor: | Koenker, Roger, Mizera, Ivan |
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| Rok vydání: | 2010 |
| Předmět: | |
| Zdroj: | Annals of Statistics 2010, Vol. 38, No. 5, 2998-3027 |
| Druh dokumentu: | Working Paper |
| DOI: | 10.1214/10-AOS814 |
| Popis: | Maximum likelihood estimation of a log-concave probability density is formulated as a convex optimization problem and shown to have an equivalent dual formulation as a constrained maximum Shannon entropy problem. Closely related maximum Renyi entropy estimators that impose weaker concavity restrictions on the fitted density are also considered, notably a minimum Hellinger discrepancy estimator that constrains the reciprocal of the square-root of the density to be concave. A limiting form of these estimators constrains solutions to the class of quasi-concave densities. Comment: Published in at http://dx.doi.org/10.1214/10-AOS814 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org) |
| Databáze: | arXiv |
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