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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Bibliographic Details
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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Summary: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.)
ISSN:0035-9246
1369-7412
2517-6161
1467-9868
DOI:10.1111/j.2517-6161.1966.tb00622.x