Estimation in autoregressive model with measurement error
ESAIM: Probability and Statistics, Volume 18 (2014), pp. 277-307.

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 θ ^ of θ 0 , for a large class of regression functions and various noise distributions.

DOI: 10.1051/ps/2013037
Classification: 62J02, 62F12, 62G05, 62G20
Keywords: autoregressive model, Markov chain, mixing, deconvolution, semi-parametric model
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Dedecker, Jérôme; Samson, Adeline; Taupin, Marie-Luce. Estimation in autoregressive model with measurement error. ESAIM: Probability and Statistics, Volume 18 (2014), pp. 277-307. doi : 10.1051/ps/2013037. http://archive.numdam.org/articles/10.1051/ps/2013037/

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