Nonparametric estimation of the chaotic function and the invariant measure of a dynamical system

D. Bosq and Dominique Guegan ()
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D. Bosq: LSTA - Laboratoire de Statistique Théorique et Appliquée - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique
Dominique Guegan: CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - IP Paris - Institut Polytechnique de Paris - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - IP Paris - Institut Polytechnique de Paris - CNRS - Centre National de la Recherche Scientifique

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Abstract: Let (Xt), Image be Image valued stochastic process defined by a discrete time dynamical system as Xt = phi(Xt−1, T = 1,2,..., where phi is some nonlinear function preserving a probability measure say μ, we estimate phi and the density -f of μ without using special condition on the analytical form of phi, with nonparametric methods and some convergence rates are given.

Keywords: Nonparametric estimation; chaotic function; invariant measure of a dynamical system (search for similar items in EconPapers)
Date: 1995-11
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Citations: View citations in EconPapers (6)

Published in Statistics and Probability Letters, 1995, 25 (3), pp.201-212. ⟨10.1016/0167-7152(94)00223-U⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00199345

DOI: 10.1016/0167-7152(94)00223-U

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