Abstract #301263

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JSM 2003 Abstract #301263
Activity Number: 331
Type: Contributed
Date/Time: Wednesday, August 6, 2003 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract - #301263
Title: Computing Maximum Likelihood Estimators of Log-Concave Density Functions
Author(s): Kaspar Rufibach*+
Companies: University of Bern, Switzerland
Address: Institut für mathematische Statistik und Versicherungslehre, Berne, , 3012, Switzerland
Keywords: interior point method ; maximum likelihood estimation ; density estimation ; convex optimization
Abstract:

We consider the problem of estimating a density that is assumed to be log-concave. Then the maximum likelihood estimator is the solution of a linearly constrained convex optimisation problem. We show that interior point algorithms perform well on this class of optimization problem for small to moderate sample sizes. As a second approach for this specific problem, we propose an optimization algorithm using the pool-adjacent violaters algorithm. Finally, we illustrate the typical shape of the estimated log-density--a piecewise linear function with only a few knots--and comment on its statistical properties.

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