Asymptotic separation in bilinear models

Abstract

This paper presents a generalisation of a non classical decision procedure for simple bilinear models with a general error process proposed by Gon calves Jacob and Mendes Lopes This decision method involves two hypotheses on the model and its consis tence is obtained by establishing the asymptotic separation of the sequences of probability laws de ned by each hypothesis Studies on the rate of convergence in the diagonal case are presented and an exponential decay is obtained Simulation experiments are used to illustrate the behaviour of the power and level functions in small and moderate samples when this procedure is used as a test