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
Keywords:
Hellinger consistency
,
Iterative concave majorant algorithm
,
Polya frequency function
Rights: Copyright © 2007, Institute of Mathematical Statistics
