Estimation in autoregressive model with measurement error. (3rd October 2014) - Dedecker, JÃ©rÃ´me
Abstract Consider an autoregressive model with measurement error: we observe Zi = Xi + Îµi, where the unobserved Xi is a stationary solution of the autoregressive equation Xi = gÎ¸0(Xi âˆ' 1) + Î¾i. The regression function gÎ¸0 is known up to a finite dimensional parameter Î¸0 to be estimated. The distributions of Î¾1 and X0 are unknown and gÎ¸ belongs to a large class of parametric regression functions. The distribution of Îµ0 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{$\hat \theta$} <textual-form>Î¸Ì‚</textual-form> of Î¸0, for a large class of regression functions and various noise distributions.