Estimation in autoregressive model with measurement error. (3rd October 2014)

• Record Type: Journal Article
• Authors: Dedecker, Jérôme; Samson, Adeline; Taupin, Marie-Luce
• Is Part Of: ESAIM. Volume 18(2014)
• Page Start: 277
• Page End: 307
• Publication Date: 2014-10-03
• Subjects: Autoregressive model, -- Markov chain, -- mixing, -- deconvolution, -- semi–parametric model; Probabilities -- Periodicals; Mathematical statistics -- Periodicals; 519.2
• DOI: 10.1051/ps/2013037
• Languages: English
• ISSNs: 1292-8100

Abstract

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{$\hat \theta$} θ̂ of θ 0, for a large class of regression functions and various noise distributions.