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June, 1969 Hypothesis Testing with Finite Statistics
Thomas M. Cover
Ann. Math. Statist. 40(3): 828-835 (June, 1969). DOI: 10.1214/aoms/1177697590


Let $X_1, X_2, \cdots$ be a sequence of independent identically distributed random variables drawn according to a probability measure $\mathscr{P}$. The two-hypothesis testing problem $H_0: \mathscr{P} = \mathscr{P}_0 \operatorname{vs.} H_1: \mathscr{P} = \mathscr{P}_1$ is investigated under the constraint that the data must be summarized after each observation by an $m$-valued statistic $T_n\varepsilon \{1, 2, \cdots, m\}$, where $T_n$ is updated according to the rule $T_{n+1} = f_n(T_n, X_{n+1})$. An algorithm with a four-valued statistic is described which achieves a limiting probability of error zero under either hypothesis. It is also demonstrated that a four-valued statistic is sufficient to resolve composite hypothesis testing problems which may be reduced to the form $H_0:p > p_0 \operatorname{vs.} H_1:p < p_0$ where $X_1, X_2, \cdots$ is a Bernoulli sequence with bias $p$.


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Thomas M. Cover. "Hypothesis Testing with Finite Statistics." Ann. Math. Statist. 40 (3) 828 - 835, June, 1969.


Published: June, 1969
First available in Project Euclid: 27 April 2007

zbMATH: 0181.45502
MathSciNet: MR240906
Digital Object Identifier: 10.1214/aoms/1177697590

Rights: Copyright © 1969 Institute of Mathematical Statistics


Vol.40 • No. 3 • June, 1969
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