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March, 1977 Weak Convergence of Processes Related to Likelihood Ratios
W. J. Hall, R. M. Loynes
Ann. Statist. 5(2): 330-341 (March, 1977). DOI: 10.1214/aos/1176343798


Material in Chapter VI of Hajek and Sidak's book is extended to a sequential analysis setting: conditions are given under which a sequence of log-likelihood-ratio processes (log-likelihood-ratios for sequential sampling, represented as jump processes in continuous time) converges weakly to a Wiener process with drift, the drift parameter depending on which hypothesis, in a suitable neighborhood of a null hypothesis, prevails. Conditions for convergence of other "test statistic" processes, related to likelihood ratios, are also given. Asymptotic sequential tests can thereby be constructed. Some "two-sample problem" examples are treated.


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W. J. Hall. R. M. Loynes. "Weak Convergence of Processes Related to Likelihood Ratios." Ann. Statist. 5 (2) 330 - 341, March, 1977.


Published: March, 1977
First available in Project Euclid: 12 April 2007

zbMATH: 0361.62074
MathSciNet: MR443254
Digital Object Identifier: 10.1214/aos/1176343798

Primary: 62L10
Secondary: 60F05 , 62E20

Keywords: Le Cam's lemmas , likelihood ratios , sequential analysis , Sign test , two-sample problem , weak convergence

Rights: Copyright © 1977 Institute of Mathematical Statistics


Vol.5 • No. 2 • March, 1977
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