Open Access
July, 1975 Exponentially Bounded Stopping Time of the Sequential t-Test
R. A. Wijsman
Ann. Statist. 3(4): 1006-1010 (July, 1975). DOI: 10.1214/aos/1176343204


Let N be the stopping time of the sequential t-test, based on the i.i.d. sequence $Z_1,Z_2,...$, for testing that the ratio of mean to standard deviation in a normal population equals $\gamma_1$ agaist the alternative that it equals $\gamma_2$. Let P be the actual distribution of the $Z_i$ (not necessarily normal). It is proved that if $\gamma_1^2\neq\gamma_2^2$ and P is an arbitrary unbounded distribution, then there exist constants c > 0 and $\rho<1$ such that $P(N > n) < c\rho^n, n =1,2,\cdots$.


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R. A. Wijsman. "Exponentially Bounded Stopping Time of the Sequential t-Test." Ann. Statist. 3 (4) 1006 - 1010, July, 1975.


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

zbMATH: 0313.62062
MathSciNet: MR411076
Digital Object Identifier: 10.1214/aos/1176343204

Primary: 62L10
Secondary: 62A05

Keywords: exponentially bounded , F05 , sequential t-test , stopping time

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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