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July, 1975 A Note on First Exit Times with Applications to Sequential Analysis
Tze Leung Lai
Ann. Statist. 3(4): 999-1005 (July, 1975). DOI: 10.1214/aos/1176343203


In this paper, we prove certain theorems about the first exit time $N=inf{n\geqq1:S_nT_n+R_n\not\in(-a,b)}$, where $S_n$ is the partial sum of i.i.d. random variables with zero mean and finite positive variance, and $R_n,T_n$ are two sequences of random variables satisfying certain conditions. Such exit times arise in the analysis of the stopping rules of invariant sequential probability ratio tests, and our theorems are then applied to study the stopping rules of these tests.


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Tze Leung Lai. "A Note on First Exit Times with Applications to Sequential Analysis." Ann. Statist. 3 (4) 999 - 1005, July, 1975.


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

zbMATH: 0342.62054
MathSciNet: MR378299
Digital Object Identifier: 10.1214/aos/1176343203

Keywords: 6245 , asymptotic behavior of moments , First exit times , Invariant sequential probability ratio tests , last time , sequential t-test

Rights: Copyright © 1975 Institute of Mathematical Statistics

Vol.3 • No. 4 • July, 1975
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