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March, 1982 Bounds on Mixtures of Distributions Arising in Order Restricted Inference
Tim Robertson, F. T. Wright
Ann. Statist. 10(1): 302-306 (March, 1982). DOI: 10.1214/aos/1176345713


In testing hypotheses involving order restrictions on a collection of parameters, distributions arise which are mixtures of standard distributions. Since tractable expressions for the mixing proportions generally do not exist even for parameter collections of moderate size, the implementation of these tests may be difficult. Stochastic upper and lower bounds are obtained for such test statistics in a variety of these kinds of problems. These bounds are also shown to be tight. The tightness results point out some situations in which the bounds could be used to obtain approximate methods. These results can also be applied to obtain the least favorable configuration when testing the equality of two multinomial populations versus a stochastic ordering alternative.


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Tim Robertson. F. T. Wright. "Bounds on Mixtures of Distributions Arising in Order Restricted Inference." Ann. Statist. 10 (1) 302 - 306, March, 1982.


Published: March, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0481.62016
MathSciNet: MR642742
Digital Object Identifier: 10.1214/aos/1176345713

Primary: 62E15
Secondary: 62G10

Keywords: $E$-bar-squared distribution , Chi-bar-squared distribution , least favorable configurations , Order restricted inference , tail probability bounds , tests for and against a trend

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 1 • March, 1982
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