Journal article
Maximum likelihood estimates with order restrictions on probabilities and odds ratios: A geometric programming approach
Journal of applied mathematics & decision sciences, Vol.1(1), pp.53-65
01/01/1997
DOI: 10.1155/S1173912697000059
Abstract
The problem of assigning cell probabilities to maximize a multinomial likelihood with order restrictions on the probabilies and/or restrictions on the local odds ratios is modeled as a posynomial geometric program (GP), a class of nonlinear optimization problems with a well-developed duality theory and collection of algorithms. (Local odds ratios provide a measure of association between categorical random variables.) A constrained multinomial MLE example from the literature is solved, and the quality of the solution is compared with that obtained by the iterative method of El Barmi and Dykstra, which is based upon Fenchel duality. Exploiting the proximity of the GP model of MLE problems to linear programming (LP) problems, we also describe as an alternative, in the absence of special-purpose GP software, an easily implemented successive LP approximation method for solving this class of MLE problems using one of the readily available LP solvers.
Details
- Title: Subtitle
- Maximum likelihood estimates with order restrictions on probabilities and odds ratios: A geometric programming approach
- Creators
- D. L. Bricker - University of IowaK. O. Kortanek - University of IowaL. Xu - Milliman
- Resource Type
- Journal article
- Publication Details
- Journal of applied mathematics & decision sciences, Vol.1(1), pp.53-65
- DOI
- 10.1155/S1173912697000059
- ISSN
- 1173-9126
- eISSN
- 1532-7612
- Number of pages
- 13
- Language
- English
- Date published
- 01/01/1997
- Academic Unit
- Industrial and Systems Engineering; Business Analytics
- Record Identifier
- 9984963200202771
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