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Estimation in autoregressive model with measurement error
Published online by Cambridge University Press: 03 October 2014
Abstract
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 \hbox{$\hat \theta$}θ̂ of θ0, for a large class of regression
functions and various noise distributions.
- Type
- Research Article
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- Copyright
- © EDP Sciences, SMAI 2014
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