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Estimation in autoregressive model with measurementerror

Published online by Cambridge University Press:  03 October 2014

Jérôme Dedecker ,
Adeline Samson  and
Marie-Luce Taupin
Jérôme Dedecker
Affiliation:
Laboratoire MAP5 UMR CNRS 8145, Université Paris Descartes, Sorbonne Paris Cité, Paris cedex 6, France
Adeline Samson
Affiliation:
Laboratoire MAP5 UMR CNRS 8145, Université Paris Descartes, Sorbonne Paris Cité, Paris cedex 6, France
Marie-Luce Taupin
Affiliation:
Laboratoire Statistique et Génome, UMR CNRS 8071-USC INRA, Université d’Évry Val d’Essonne, Évry, France. [email protected]
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Abstract

Consider an autoregressive model with measurement error: we observe Zi =Xi +εi, where theunobserved Xi is a stationarysolution of the autoregressive equation Xi =gθ0(Xi− 1) + ξi. Theregression function gθ0 isknown up to a finite dimensional parameter θ0 to be estimated. The distributions ofξ1 and X0 are unknownand gθ belongs to a largeclass of parametric regression functions. The distribution of ε0 is completelyknown. We propose an estimation procedure with a new criterion computed as the Fouriertransform of a weighted least square contrast. This procedure provides an asymptoticallynormal estimator \hbox{$\hat \theta$}θ̂ of θ0, for a large class of regressionfunctions and various noise distributions.

Keywords

Autoregressive modelMarkov chainmixingdeconvolutionsemi–parametric model
Type
Research Article
Information
ESAIM: Probability and Statistics , Volume 18 , 2014 , pp. 277 - 307
Copyright
© EDP Sciences, SMAI 2014

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