Asymptotic local test for linearity in adaptive control

This paper deals with an asymptotic local test for linearity of nonlinear dynamical systems. The aim of the test is to compare two estimators of the leading function of the dynamical system, built with the observations contained in a fixed domain . The first one is naturally local since it is a kernel-based estimator. The second one is a -localized version of the least squares estimator. We prove a convergence result, including rate, for the latter estimator and deduce a central limit theorem leading to an asymptotic test. Some simulations illustrate the need of such a local procedure and investigate the finite sample case.