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July, 1975 A Finite Memory Test of the Irrationality of the Parameter of a Coin
Patrick Hirschler, Thomas M. Cover
Ann. Statist. 3(4): 939-946 (July, 1975). DOI: 10.1214/aos/1176343194

Abstract

Let $X_1,X_2,...$ be a Bernoulli sequence with parameter p. An algorithm $T_{n=1}=\\f(T_n,X_n,n)$; $d_n = d(T_n); \\f:\{1,2,\1dots,8\} \times \{0,1\} \times \{0,1, \1dots}\rightarrow \{1, \1dots, 8\}; d:\{1,2,\dots,8\} \rigtharrow \{H_0,H_1\}$; is found such that $d(T_n)= H_0$ all but a finite number of times with probability one if p is rational, and $d(T_n)= H_1$ all but a finite number of times with probability one if p is irrational (and not in a given null set of irrationals). Thus, an 8-state memory with a time-varying algorithm makes only a finite number of mistakes with probability one on determining the rationality of the parameter of a coin. Thus, determining the rationality of the Bernoulli parameter p does not depend on infinite memory of the data.

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Patrick Hirschler. Thomas M. Cover. "A Finite Memory Test of the Irrationality of the Parameter of a Coin." Ann. Statist. 3 (4) 939 - 946, July, 1975. https://doi.org/10.1214/aos/1176343194

Information

Published: July, 1975
First available in Project Euclid: 12 April 2007

zbMATH: 0325.62010
MathSciNet: MR388695
Digital Object Identifier: 10.1214/aos/1176343194

Subjects:
Primary: 62C99

Keywords: coin , Finite memory , Hypothesis testing , rationals

Rights: Copyright © 1975 Institute of Mathematical Statistics

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Vol.3 • No. 4 • July, 1975
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