Abstract
Suppose it is desired to make one of two decisions, d 1 and d 2, on the basis of independent observations on a chance variable whose distribution F is known to belong to a set F. There are given two subsets G and H of F such that decision d 1(d 2) is strongly preferred if F is in G (H). Then it is reasonable to look for a test (decision rule) which makes the probability of an erroneous decision small when F belongs to G or H, and at the same time exercises some control over the number of observations required to reach a decision when F is in F (not only in G or H).
The research of this author was supported by the United States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command, under contract No. AF 18(600)-685. Reproduction in whole or in part is permitted for any purpose of the United States Government.
The research of this author was supported by the Uni ted States Air Force through the Air Force Office of Scientific Research of the Air Research and Development Command. und er contract No. AF 18(600)-458. Reproduction in whole or in part is permitted for any purpose of the United States Government.
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References
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Hoeffding, W., Wolfowitz, J. (1994). Distinguishability of Sets of Distributions. In: Fisher, N.I., Sen, P.K. (eds) The Collected Works of Wassily Hoeffding. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0865-5_21
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DOI: https://doi.org/10.1007/978-1-4612-0865-5_21
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