Bruno Portier

Partial and Recombined Estimators for Nonlinear Additive Models

Starting from a variant of an estimator using marginal integration, this paper proposes partial and recombined estimators for nonlinear additive regression models. Partial estimators are used for data analysis purposes and recombined estimators are used to improve the estimation and prediction performances for small to moderate sample sizes. In the first part of the paper, some simulations illustrate step-by-step the principle and the value of the proposed estimators, which are finally applied to the analysis and prediction of ozone concentration in Paris area. In the second part of the paper, almost sure convergence results as well as a multivariate central limit theorem and a test for partial additivity are provided.

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.

Estimation and test of linearity for a class of additive nonlinear models

This paper deals with the estimation and the test for linearity of models belonging to a class of additive nonlinear ones. We prove the joint asymptotic normality for a kernel estimator and provide a test for linearity of each function defining the model.

Testing Linearity for NARX Models

We propose to test the linearity of dynamical systems described by discrete-time NARX models. Such non-parametric models are flexible and therefore especially convenient for specification and identification purposes. A test of linearity allows to decide if it is necessary to use a non-linear model rather than a classical linear one. The key idea of our test is to use and compare a kernel estimator and a least-squares estimator. The test statistic is based on a sum of quadratic deviations between these estimators and has a χ2 limiting distribution under the null hypothesis.