Estimation in autoregressive model with measurement error. (3rd October 2014) - Dedecker, JÃ©rÃ´me; Samson, Adeline; Taupin, Marie-Luce
<x content-type="archive" xml:space="preserve">Abstract</x> 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 <alternatives> <![CDATA[\hbox{$\hat \theta$}]]> <inline-graphic mimetype="image" xlink:href="ark:/27927/pgjcgr3rhj" xmlns:xlink="http://www.w3.org/1999/xlink" /><textual-form>Î¸Ì‚</textual-form></alternatives> of Î¸0, for a large class of regression functions and various noise distributions.