Asymptotic approximations for the error probabilities of
sequential tests of composite hypotheses in multiparameter exponential families
are developed herein for a general class of test statistics, including
generalized likelihood ratio statistics and other functions of the sufficient
statistics. These results not only generalize previous approximations for Type
I error probabilities of sequential generalized likelihood ratio tests, but
also pro- vide a unified treatment of both sequential and fixed sample size
tests and of Type I and Type II error probabilities. Geometric arguments
involving integration over tubes play an important role in this unified
theory.
Publié le : 2000-12-14
Classification:
Sequential generalized likelihood ratio tests,
Bayes sequential tests,
multiparameter exponential families,
boundary crossing probabilities,
integration over tubes,
62L10,
62L15,
62E20,
60F10,
49Q15
@article{1015957474,
author = {Chan, Hock Peng and Lai, Tze Leung},
title = {Asymptotic approximations for error probabilities of sequential
or fixed sample size tests in exponential families},
journal = {Ann. Statist.},
volume = {28},
number = {3},
year = {2000},
pages = { 1638-1669},
language = {en},
url = {http://dml.mathdoc.fr/item/1015957474}
}
Chan, Hock Peng; Lai, Tze Leung. Asymptotic approximations for error probabilities of sequential
or fixed sample size tests in exponential families. Ann. Statist., Tome 28 (2000) no. 3, pp. 1638-1669. http://gdmltest.u-ga.fr/item/1015957474/