Issue |
ESAIM: PS
Volume 18, 2014
|
|
---|---|---|
Page(s) | 277 - 307 | |
DOI | https://doi.org/10.1051/ps/2013037 | |
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
marie-luce.taupin@genopole.cnrs.fr
Received:
24
October
2011
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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