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Estimation in autoregressive model with measurement error

Abstract : Consider an autoregressive model with measurement error: we observe Z(i) = X-i + epsilon(i), where the unobserved X-i is a stationary solution of the autoregressive equation X-i = g(theta 0) (Xi- 1) + xi(i). The regression function g(theta 0) is known up to a finite dimensional parameter theta(0) to be estimated. The distributions of xi(1) and X-0 are unknown and g(theta) belongs to a large class of parametric regression functions. The distribution of epsilon(0) 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 (theta) over cap of theta(0), for a large class of regression functions and various noise distributions.
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Jérôme Dedecker, Adeline Samson, Marie-Luce Taupin. Estimation in autoregressive model with measurement error. ESAIM: Probability and Statistics, 2014, 18, pp.277-307. ⟨10.1051/ps/2013037⟩. ⟨hal-02633693⟩



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