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May, 1974 On the Maximum Likelihood Estimation of Stochastically Ordered Random Variates
Tim Robertson, F. T. Wright
Ann. Statist. 2(3): 528-534 (May, 1974). DOI: 10.1214/aos/1176342712


Brunk, Franck, Hanson and Hogg (1966) ("Maximum likelihood estimation of the distributions of two stochastically ordered random variables," J. Amer. Statist. Assoc. 61 1067-1080) found and studied maximum likelihood estimates of a pair of stochastically ordered distribution functions. In this paper we discuss a generalization of this problem in which we do not require the domain of these "distribution functions" to be the real line. We think of the order restriction we impose on these "distribution functions" as an analogue of stochastic ordering on the line. Maximum likelihood estimates are found and strong uniform consistency properties are discussed.


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Tim Robertson. F. T. Wright. "On the Maximum Likelihood Estimation of Stochastically Ordered Random Variates." Ann. Statist. 2 (3) 528 - 534, May, 1974.


Published: May, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0301.62021
MathSciNet: MR388641
Digital Object Identifier: 10.1214/aos/1176342712

Primary: 62G05
Secondary: 60F15

Keywords: consistency , maximum likelihood estimation , stochastic ordering

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 3 • May, 1974
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