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Biometrika 1974 61(2):361-368; doi:10.1093/biomet/61.2.361
© 1974 by Biometrika Trust
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A class of optimal stopping problems for sampling without replacement

DONALD A. BERRY

Department of Theoretical Statistics, University of Minnesota Minneapolis

It is required to estimate exactly the number r of red balls in a population of n balls. The initial distribution of r is uniform on 0, ...,n and further information can be obtained by sampling the balls sequentially without replacement at a cost of (i) 1, (ii) k, (iii) k2 for the kth ball. The problem is normalized by setting the optimal expected payoff for estimating prior to sampling and for estimating after sampling all n balls both equal to zero. Asymptotically as n {uparrow} {infty} optimal stopping rules are found. Dynamic programs are carried out for n = 15.

Key Words: Bayesian decision theory • Dynamic programming • Maximum likelihood estimation • Optimal stopping • Sequential sampling • Urn models


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