The Annals of Statistics

Convergence of Simar's Algorithm for Finding the Maximum Likelihood Estimate of a Compound Poisson Process

Dankmar Bohning

Abstract

Simar (1976) suggested an iteration procedure for finding the maximum likelihood estimate of a compound Poisson process, but he could not show convergence. Here the more general case of maximizing a concave functional on the set of all probability measures is treated. As a generalization of Simar's procedure, an algorithm is given for solving this problem, including assumptions to ensure convergence to an optimum. Finally, it is shown that Simar's functional fulfills these assumptions.

Article information

Source
Ann. Statist. Volume 10, Number 3 (1982), 1006-1008.

Dates
First available in Project Euclid: 12 April 2007

http://projecteuclid.org/euclid.aos/1176345890

Digital Object Identifier
doi:10.1214/aos/1176345890

Mathematical Reviews number (MathSciNet)
MR663451

Zentralblatt MATH identifier

Subjects
Primary: 62G05: Estimation
Secondary: 62M99: None of the above, but in this section

Citation

Bohning, Dankmar. Convergence of Simar's Algorithm for Finding the Maximum Likelihood Estimate of a Compound Poisson Process. Ann. Statist. 10 (1982), no. 3, 1006--1008. doi:10.1214/aos/1176345890. http://projecteuclid.org/euclid.aos/1176345890.