Maximum likelihood estimation of ordered multinomial probabilities by geometric programming

We propose an efficient method to compute the maximum likelihood estimator of ordered multinomial probabilities. Using the monotonicity property of the likelihood function, we reformulate the estimation problem as a geometric program, a special type of mathematical optimization problem, which can be...

Full description

Saved in:
Bibliographic Details
Published in:Computational statistics & data analysis 2009-02, Vol.53 (4), p.889-893
Main Authors: Lim, Johan, Wang, Xinlei, Choi, Wanseok
Format: Article
Language:English
Subjects:
Differential geometry
Exact sciences and technology
General topics
Geometry
Mathematics
Multivariate analysis
Numerical analysis
Numerical analysis. Scientific computation
Numerical methods in probability and statistics
Probability and statistics
Sciences and techniques of general use
Statistics
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:We propose an efficient method to compute the maximum likelihood estimator of ordered multinomial probabilities. Using the monotonicity property of the likelihood function, we reformulate the estimation problem as a geometric program, a special type of mathematical optimization problem, which can be transformed into a convex optimization problem, and then solved globally and efficiently. We implement a numerical study to illustrate its computational merits in comparison to the m-PAV algorithm proposed by [Jewell, N.P., Kalbfleisch, J., 2004. Maximum likelihood estimation of ordered multinomial parameters. Biostatistics 5, 291–306]. We also apply our proposed method to the current status data in the above mentioned reference.
ISSN:0167-9473
1872-7352
DOI:10.1016/j.csda.2008.10.021