Estimating a Polya frequency function_2

Details Estimating a Polya frequency function_2 Estimating a Polya frequency function_2

2007-08-08

arxiv.org/abs/0708.1064v1

IMS Lecture Notes Monograph Series 2007, Vol. 54, 239-249

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/074921707000000184 in the IMS Lecture Notes Monograph Series (http://www.imstat.org/p

Scientific paper

10.1214/074921707000000184

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.

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