Quasi-concave density estimation

Details Quasi-concave density estimation Quasi-concave density estimation

2010-07-22

arxiv.org/abs/1007.4013v2

Annals of Statistics 2010, Vol. 38, No. 5, 2998-3027

Statistics

Methodology

Published in at http://dx.doi.org/10.1214/10-AOS814 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of

Scientific paper

10.1214/10-AOS814

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.

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