Estimating a Polya frequency function_2

Abstract

We consider the non-parametric maximum likelihood estimation in the class of Polya frequency functions of order two, viz. the densities with a concave logarithm. This is a subclass of unimodal densities and fairly rich in general. The NPMLE is shown to be the solution to a convex programming problem in the Euclidean space and an algorithm is devised similar to the iterative convex minorant algorithm by Jongbleod (1999). The estimator achieves Hellinger consistency when the true density is a PFF_2 itself.Comment: Published at http://dx.doi.org/10.1214/074921707000000184 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org