A Non-Parametric Test for Non-Independent Noises Against a Bilinear Dependence

Abstract

A new methodology, based on the asymptotic separation of probability laws, was introduced by Gonçalves, Jacob and Mendes-Lopes (2000) in the development of the statistical inference of bilinear models, namely in the construction of a consistent decision procedure for the simple bilinear ones. This paper presents a generalisation of that study by introducing in the procedure a smoother decision statistics. The aim of this decision method is to discriminate between an error process and a simple bilinear model. So, we use it as a consistent test, its consistence being obtained by establishing the asymptotic separation of the sequences of probability laws defined by each hypothesis. The convergence rate of the procedure is studied under the truthfulness of the error process hypothesis. An exponential decay is obtained.