  In this paper, a modification of the conventional approximations to the
quasi-maximum likelihood method is introduced for the parameter estimation of
diffusion processes from discrete observations. This is based on a convergent
approximation to the first two conditional moments of the diffusion process
through discrete-time schemes. It is shown that, for finite samples, the
resulting approximate estimators converge to the quasi-maximum likelihood one
when the error between the discrete-time approximation and the diffusion
process decreases. For an increasing number of observations, the approximate
estimators are asymptotically normal distributed and their bias decreases when
the mentioned error does it. A simulation study is provided to illustrate the
performance of the new estimators. The results show that, with respect to the
conventional approximate estimators, the new ones significantly enhance the
parameter estimation of the test equations. The proposed estimators are
intended for the recurrent practical situation where a nonlinear stochastic
system should be identified from a reduced number of complete observations
distant in time.
