The Annals of Statistics

On the Maximum Likelihood Estimation of Stochastically Ordered Random Variates

Tim Robertson and F. T. Wright

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Abstract

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.

Article information

Source
Ann. Statist., Volume 2, Number 3 (1974), 528-534.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176342712

Digital Object Identifier
doi:10.1214/aos/1176342712

Mathematical Reviews number (MathSciNet)
MR388641

Zentralblatt MATH identifier
0301.62021

JSTOR
links.jstor.org

Subjects
Primary: 62G05: Estimation
Secondary: 60F15: Strong theorems

Keywords
Stochastic ordering maximum likelihood estimation consistency

Citation

Robertson, Tim; Wright, F. T. On the Maximum Likelihood Estimation of Stochastically Ordered Random Variates. Ann. Statist. 2 (1974), no. 3, 528--534. doi:10.1214/aos/1176342712. https://projecteuclid.org/euclid.aos/1176342712


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