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.
@article{1176343798,
author = {Hall, W. J. and Loynes, R. M.},
title = {Weak Convergence of Processes Related to Likelihood Ratios},
journal = {Ann. Statist.},
volume = {5},
number = {1},
year = {1977},
pages = { 330-341},
language = {en},
url = {http://dml.mathdoc.fr/item/1176343798}
}
Hall, W. J.; Loynes, R. M. Weak Convergence of Processes Related to Likelihood Ratios. Ann. Statist., Tome 5 (1977) no. 1, pp. 330-341. http://gdmltest.u-ga.fr/item/1176343798/