The Maximum Likelihood Estimates of Multinomial Parameters Subject to Stochastic Order with Equality
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Date
1999-10-??-
Authors
張少同
呂小娟
Shao-Tung Chang and Hsiao-Chuan Lu
Journal Title
Journal ISSN
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Publisher
國立臺灣師範大學研究發展處
Office of Research and Development
Office of Research and Development
Abstract
長久以來，有關隨機序的估計問題一直被廣泛的討論與應用，然而在許多實際的應用上，我們發現兩組多項式分配的參數p和q除了隨機之外，可能還有其他的關係，例如相等、相差一個常數，或是成倍數關係。我們對參數了解愈多，愈能夠得到更精確的估計，因而在文章中，我們仿效Barlow及Brunk（1972）的方法推得在隨機序與部分等式條件下，多項式參數的最大概似估計。我們依單樣本和雙樣本分別討論並提供應用實例，此外我們也探討估計的一致性問題。
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.
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.