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Asymptotic local test for linearity in adaptive control

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  • Poggi, Jean-Michel
  • Portier, Bruno
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    Abstract

    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.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 55 (2001)
    Issue (Month): 1 (November)
    Pages: 9-17

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    Handle: RePEc:eee:stapro:v:55:y:2001:i:1:p:9-17

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    Related research

    Keywords: Adaptive control Discrete-time stochastic nonlinear system Kernel estimation Test for linearity Local least squares estimator;

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