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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
Published by: Institute of Mathematical Statistics
Stable URL: http://www.jstor.org/stable/20461472
Page Count: 11
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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 PFF₂ itself.
Lecture Notes-Monograph Series © 2007 Institute of Mathematical Statistics