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Estimating a Polya Frequency Function₂

Jayanta Kumar Pal, Michael Woodroofe and Mary Meyer
Lecture Notes-Monograph Series
Vol. 54, Complex Datasets and Inverse Problems: Tomography, Networks and Beyond (2007), pp. 239-249
Stable URL: http://www.jstor.org/stable/20461472
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Estimating a Polya Frequency Function₂
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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 PFF₂ itself.

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