Volume 18, 2014
|Page(s)||277 - 307|
|Published online||03 October 2014|
Estimation in autoregressive model with measurement error
1 Laboratoire MAP5 UMR CNRS 8145, Université Paris Descartes,
Sorbonne Paris Cité, Paris cedex 6, France
2 Laboratoire Statistique et Génome, UMR CNRS 8071-USC INRA, Université d’Évry Val d’Essonne, Évry, France
Revised: 14 February 2013
Consider an autoregressive model with measurement error: we observe Zi = Xi + εi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gθ0(Xi − 1) + ξi. The regression function gθ0 is known up to a finite dimensional parameter θ0 to be estimated. The distributions of ξ1 and X0 are unknown and gθ belongs to a large class of parametric regression functions. The distribution of ε0 is completely known. We propose an estimation procedure with a new criterion computed as the Fourier transform of a weighted least square contrast. This procedure provides an asymptotically normal estimator of θ0, for a large class of regression functions and various noise distributions.
Mathematics Subject Classification: 62J02 / 62F12 / 62G05 / 62G20
Key words: Autoregressive model / Markov chain / mixing / deconvolution / semi–parametric model
© EDP Sciences, SMAI 2014
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