Consider an autoregressive model with measurement error: we observe , where the unobserved is a stationary solution of the autoregressive equation . The regression function is known up to a finite dimensional parameter to be estimated. The distributions of and are unknown and belongs to a large class of parametric regression functions. The distribution of 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 of , for a large class of regression functions and various noise distributions.
Keywords: autoregressive model, Markov chain, mixing, deconvolution, semi-parametric model
@article{PS_2014__18__277_0, author = {Dedecker, J\'er\^ome and Samson, Adeline and Taupin, Marie-Luce}, title = {Estimation in autoregressive model with measurement error}, journal = {ESAIM: Probability and Statistics}, pages = {277--307}, publisher = {EDP-Sciences}, volume = {18}, year = {2014}, doi = {10.1051/ps/2013037}, language = {en}, url = {http://archive.numdam.org/articles/10.1051/ps/2013037/} }
TY - JOUR AU - Dedecker, Jérôme AU - Samson, Adeline AU - Taupin, Marie-Luce TI - Estimation in autoregressive model with measurement error JO - ESAIM: Probability and Statistics PY - 2014 SP - 277 EP - 307 VL - 18 PB - EDP-Sciences UR - http://archive.numdam.org/articles/10.1051/ps/2013037/ DO - 10.1051/ps/2013037 LA - en ID - PS_2014__18__277_0 ER -
%0 Journal Article %A Dedecker, Jérôme %A Samson, Adeline %A Taupin, Marie-Luce %T Estimation in autoregressive model with measurement error %J ESAIM: Probability and Statistics %D 2014 %P 277-307 %V 18 %I EDP-Sciences %U http://archive.numdam.org/articles/10.1051/ps/2013037/ %R 10.1051/ps/2013037 %G en %F PS_2014__18__277_0
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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