Janis Hardwick
Connie Page
Michigan State University
Quentin F. Stout
University of Michigan
Information maximization considerations, and analysis of the asymptotic mean square error of several estimators, lead to the following adaptive procedure: use the maximum likelihood estimator to estimate p, and if this estimator is below the cut-point ar, then observe an individual trial at the next stage, while if it is above the cut-point then observe a product trial. In a Bayesian setting with squared error estimation loss and suitable regularity conditions on the prior distribution, this adaptive procedure, replacing the maximum likelihood estimator with the Bayes estimator, will be asymptotically Bayes.
Exact computational evaluations of the adaptive procedure for fixed sample sizes show that it behaves roughly as the asymptotics predict. The exact analyses also show parameter regions for which the adaptive procedure achieves negative regret, as well as regions for which it achieves normalized mean squared error superior to that asymptotically possible.
An example and a discussion of extensions conclude the work.
Keywords:
batch testing, risk assessment, infection rate,
grouped data, omniscient allocation, composite testing, adaptive design,
sequential, pooled data, design of experiments, statistics
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