SEQUENTIAL VERSIONS OF THE GENERALIZED LIKELIHOOD RATIO TEST

It is shown that the Wilks large sample likelihood ratio statistic λn, for testing between composite hypotheses [Formated text] on the basis of a sample of size n, behaves as n varies like a diffusion process related to an equilibrium Ornstein- Uhlenbeck process, whenever the null hypothesis is true. This fact is used to construct large sample sequential tests based on λn, which are the same whatever the underlying distributions. In particular, the underlying distributions need not belong to an exponential family. © 1979, Cambridge Philosophical Society. All rights reserved.