Maximum likelihood estimation of ordered multinomial probabilities by geometric programming

Johan Lim, Xinlei Wang and Wanseok Choi

Computational Statistics & Data Analysis, 2009, vol. 53, issue 4, 889-893

Abstract: 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.

Date: 2009
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