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October, 1972 A Theorem on Obstructive Distributions
R. A. Wijsman
Ann. Math. Statist. 43(5): 1709-1715 (October, 1972). DOI: 10.1214/aoms/1177692407


Let $N$ be the stopping time of a sequential probability ratio test of composite hypothesis, based on the i.i.d. sequence $Z_1, Z_2, \cdots$ with common distribution $P$. If for every choice of stopping bounds there exist constants $c > 0, 0 < \rho < 1$ such that $P\{N > n\} < c\rho^n n = 1, 2, \cdots$, we say that $N$ is exponentially bounded under $P$; otherwise $P$ is called obstructive. A theorem is proved giving sufficient conditions for $P$ to be obstructive. By virtue of this theorem it is possible to exhibit families of obstructive distributions in several examples, including the sequential $t$-test.


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R. A. Wijsman. "A Theorem on Obstructive Distributions." Ann. Math. Statist. 43 (5) 1709 - 1715, October, 1972.


Published: October, 1972
First available in Project Euclid: 27 April 2007

zbMATH: 0247.62027
MathSciNet: MR350995
Digital Object Identifier: 10.1214/aoms/1177692407

Rights: Copyright © 1972 Institute of Mathematical Statistics


Vol.43 • No. 5 • October, 1972
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