Asymptotic Sequential Design of Experiments with Two Random Variables

Given two independent random variables with densities f1 and f2, we test H1:f1=f11,f2=f12 versus H2:f1=f21,f2=f22, where the fij are known densities (i,j=1,2). We study asymptotic Bayes sequential procedures as the cost of each observation approaches zero. An asymptotic expression for the Bayes risk...

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Published in:Journal of the Royal Statistical Society. Series B, Methodological Methodological, 1966-01, Vol.28 (1), p.73-87
Main Author: Abramson, Lee R.
Format: Article
Language:English
Subjects:
Error rates
Experiment design
Mathematics
Probability distributions
Random variables
Ratio test
Sample size
Sufficient conditions
Tariff drawbacks
Variable costs
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description Given two independent random variables with densities f1 and f2, we test H1:f1=f11,f2=f12 versus H2:f1=f21,f2=f22, where the fij are known densities (i,j=1,2). We study asymptotic Bayes sequential procedures as the cost of each observation approaches zero. An asymptotic expression for the Bayes risk is found, and necessary and sufficient conditions for a decision rule to be asymptotically Bayes are derived. We study a class of tests which we call tandem tests and construct an asymptotically Bayes set of tandem tests. (A tandem test is a sequence of at most two sequential probability ratio tests, the first performed on one of the random variables and the second performed on the other.)
doi_str_mv 10.1111/j.2517-6161.1966.tb00622.x
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source JSTOR Archival Journals and Primary Sources Collection
subjects Error rates
Experiment design
Mathematics
Probability distributions
Random variables
Ratio test
Sample size
Sufficient conditions
Tariff drawbacks
Variable costs
title Asymptotic Sequential Design of Experiments with Two Random Variables
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