Institute of Mathematical Statistics Lecture Notes - Monograph Series

Estimating a Polya frequency function$_2$

Jayanta Kumar Pal, Michael Woodroofe, and Mary Meyer

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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.

Chapter information

Regina Liu, William Strawderman and Cun-Hui Zhang, eds., Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2007), 239-249

First available in Project Euclid: 4 December 2007

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Primary: 62G07: Density estimation 62G08: Nonparametric regression
Secondary: 90C25: Convex programming

Polya frequency function Iterative concave majorant algorithm Hellinger consistency

Copyright © 2007, Institute of Mathematical Statistics


Pal, Jayanta Kumar; Woodroofe, Michael; Meyer, Mary. Estimating a Polya frequency function$_2$. Complex Datasets and Inverse Problems, 239--249, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2007. doi:10.1214/074921707000000184.

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