## Institute of Mathematical Statistics Lecture Notes - Monograph Series

### Estimating a Polya frequency function$_2$

#### 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.

#### Chapter information

Source
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

Dates
First available in Project Euclid: 4 December 2007

http://projecteuclid.org/euclid.lnms/1196794956

Digital Object Identifier
doi:10.1214/074921707000000184

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

Rights
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. http://projecteuclid.org/euclid.lnms/1196794956.