2010/07/31 by Roger Koenker, Ivan Mizera
Engineering · Mathematics · Physics and Astronomy · #Density estimation #Entropy (arrow of time) #Estimator #Hellinger distance #Maximum entropy probability distribution #Maximum entropy spectral estimation #Maximum likelihood #Principle of maximum entropy #Probability density function #Rényi entropy #Statistical Mechanics and Entropy #Statistical Methods and Inference #Wireless Communication Security Techniques #math.ST #stat.ME #stat.TH
paper · pdf · doi:10.1214/10-aos814
published as Annals of Statistics 2010, Vol. 38, No. 5, 2998-3027 · 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)
openalex publication_date 2010/08/20 · arxiv created 2010/11/15 · arxiv updated 2010/11/16 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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.