Estimating a Polya frequency function2
نویسنده
چکیده
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.
منابع مشابه
Estimating a Polya Frequency Function
The problem of estimating a unimodal density and its mode has attracted a wide interest in the literature, beginning with the work of Barlow [1], Prakasa Rao, [7], Robertson, [8], and Wegman [13], [14] and continuing through [9], [2], [3], [5], and [4], who can be consulted for further references. Asymptotic properties of the maximum likelihood estimators have been developed but may be messy an...
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