The Maximum Likelihood Estimates of Multinomial Parameters Subject to Stochastic Order with Equality

Author: Shao-Tung Chang, Hsiao -Chuan Lu(Department of Applied Mathematics, Chinese Culture University)

Vol.&No.：Vol. 44, No. 1
Date：April 1999
Pages：1-9
DOI：10.6301/JNTNU.1999.44(1).01

Abstract：

The problems of maximum likelihood estimates of multinomial parameters subject to stochastic ordering have been widely discussed. However, in some applications, the multinomial parameters p and q may not only satisfy the stochastically ordered constraints but also the equality of some of these parameters. We follow Barlow and Brunk's method (1972) and obtain the Fenchel duality projection-type maximum likelihood estimates of multinomial parameters under this modified hypothesis for both one-sample and two-sample problems. The consistency of the estimates is proved and. an example is also presented as an illustration.

Keywords：Multinomial parameters, Maximum likelihood estimate, Stochastic ordering, Least square projection

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