The joint estimation of both drift and diffusion coefficient parameters is treated under the situation where the data are discretely observed from an ergodic diffusion process and where the statistical model may or may not include the true diffusion process. We consider the minimum contrast estimator, which is equivalent to the maximum likelihood type estimator, obtained from the contrast function based on a locally Gaussian approximation of the transition density. The asymptotic normality of the minimum contrast estimator is proved. In particular, the rate of convergence for the minimum contrast estimator of diffusion coefficient parameter in a misspecified model is different from the one in the correctly specified parametric model.
Mots-clés : diffusion process, misspecified model, discrete time observations, minimum contrast estimator, rate of convergence
@article{PS_2011__15__270_0, author = {Uchida, Masayuki and Yoshida, Nakahiro}, title = {Estimation for misspecified ergodic diffusion processes from discrete observations}, journal = {ESAIM: Probability and Statistics}, pages = {270--290}, publisher = {EDP-Sciences}, volume = {15}, year = {2011}, doi = {10.1051/ps/2010001}, mrnumber = {2870516}, language = {en}, url = {http://www.numdam.org/articles/10.1051/ps/2010001/} }
TY - JOUR AU - Uchida, Masayuki AU - Yoshida, Nakahiro TI - Estimation for misspecified ergodic diffusion processes from discrete observations JO - ESAIM: Probability and Statistics PY - 2011 SP - 270 EP - 290 VL - 15 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/ps/2010001/ DO - 10.1051/ps/2010001 LA - en ID - PS_2011__15__270_0 ER -
%0 Journal Article %A Uchida, Masayuki %A Yoshida, Nakahiro %T Estimation for misspecified ergodic diffusion processes from discrete observations %J ESAIM: Probability and Statistics %D 2011 %P 270-290 %V 15 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/ps/2010001/ %R 10.1051/ps/2010001 %G en %F PS_2011__15__270_0
Uchida, Masayuki; Yoshida, Nakahiro. Estimation for misspecified ergodic diffusion processes from discrete observations. ESAIM: Probability and Statistics, Tome 15 (2011), pp. 270-290. doi : 10.1051/ps/2010001. http://www.numdam.org/articles/10.1051/ps/2010001/
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