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December, 1955 Maximum Likelihood Estimates of Monotone Parameters
H. D. Brunk
Ann. Math. Statist. 26(4): 607-616 (December, 1955). DOI: 10.1214/aoms/1177728420


The maximum likelihood estimators of distribution parameters subject to certain order relations are determined for simultaneous sampling from a number of populations, when $(i)$ the order relations may be specified by regarding the distribution parameters, of which one is associated with each population, as values at specified points of a function of $n$ variables ($n$ a positive integer), monotone in each variable separately; (ii) the distributions of the populations from which sample values are taken belong to the exponential family defined below. This family includes, in particular, the binomial, the normal with fixed standard deviation and variable mean, the normal with fixed mean and variable standard deviation, and the Poisson distributions.


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H. D. Brunk. "Maximum Likelihood Estimates of Monotone Parameters." Ann. Math. Statist. 26 (4) 607 - 616, December, 1955.


Published: December, 1955
First available in Project Euclid: 28 April 2007

zbMATH: 0066.38503
MathSciNet: MR73894
Digital Object Identifier: 10.1214/aoms/1177728420

Rights: Copyright © 1955 Institute of Mathematical Statistics

Vol.26 • No. 4 • December, 1955
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