Estimation in autoregressive model with measurement error. (3rd October 2014) - Dedecker, Jérôme; Samson, Adeline; Taupin, Marie-Luce
Abstract : Consider an autoregressive model with measurement error: we observe Z i = X i + ε i, where the unobserved X i is a stationary solution of the autoregressive equation X i = g θ 0 ( X i − 1 ) + ξ i . The regression function g θ 0 is known up to a finite dimensional parameter θ 0 to be estimated. The distributions of ξ 1 and X 0 are unknown and g θ belongs to a large class of parametric regression functions. The distribution of ε 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\hbox{$\hat θ$} θ̂ of θ 0, for a large class of regression functions and various noise distributions.