Extensions of the Stochastic Ordering Property of Likelihood Ratios

Abstract

Extensions in two directions are described of the well-known stochastic ordering property of likelihood ratios. 1. It is shown that the stochastic ordering property holds in a very general conditional sense. 2. It is shown that, for the usual setting occurring in sequential analysis, sequences of likelihood ratios possess the same stochastic ordering property in a multivariate sense. Applications to sequential analysis, and elsewhere, are described.