Translator Disclaimer
VOL. 54 | 2007 Estimating a Polya frequency function$_2$
Jayanta Kumar Pal, Michael Woodroofe, Mary Meyer

Editor(s) Regina Liu, William Strawderman, Cun-Hui Zhang

## 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.

## Information

Published: 1 January 2007
First available in Project Euclid: 4 December 2007

MathSciNet: MR2459192

Digital Object Identifier: 10.1214/074921707000000184

Subjects:
Primary: 62G07, 62G08
Secondary: 90C25