Let YT = (Yt)t∈[0,T] be a real ergodic
diffusion process which drift depends on an unkown
parameter $\theta_{0}\in \mathbb{R}^{p}$. Our aim is to estimate θ0 from a discrete
observation of the process YT, (Ykδ)k=0,n, for a
fixed and small δ, as T = nδ goes to infinity. For that purpose, we
adapt the Generalized Method of Moments (see Hansen) to the anticipative
and approximate discrete-time trapezoidal scheme, and then to Simpson's.
Under some general assumptions, the trapezoidal scheme (respectively Simpson's
scheme) provides an estimation of θ0 with a bias of order δ2 (resp.
δ4). Moreover, this estimator is asymptotically normal.
These results generalize Bergstrom's [1], which were obtained for a
Gaussian diffusion process, which drift is linear in θ.