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March, 1974 Multiple Hypothesis Testing by Finite Memory Algorithms
S. Yakowitz
Ann. Statist. 2(2): 323-336 (March, 1974). DOI: 10.1214/aos/1176342666


In recent years, a theory has been emerging concerning the statistical power of small computers. In the present paper it is proven that in the sense peculiar to this literature, small computers (mathematically equivalent to finite automata) can in general be designed to solve multiple simple hypothesis testing problems. In many cases, only one state for each hypothesis is needed. In a more conventional sense, we reveal the construction of finite automata which implement sequential decision procedures having the capacity to distinguish between any given finite set of probabilities with any desired accuracy. Finally, some results on the ability of finite automata to track time--changing hypotheses are outlined.


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S. Yakowitz. "Multiple Hypothesis Testing by Finite Memory Algorithms." Ann. Statist. 2 (2) 323 - 336, March, 1974.


Published: March, 1974
First available in Project Euclid: 12 April 2007

zbMATH: 0277.62019
MathSciNet: MR363738
Digital Object Identifier: 10.1214/aos/1176342666

Primary: 62F05
Secondary: 93E10

Keywords: finite automata , finite memory distinguishability , multiple hypothesis testing

Rights: Copyright © 1974 Institute of Mathematical Statistics


Vol.2 • No. 2 • March, 1974
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