  In this paper, an alternative approximation to the innovation method is
introduced for the parameter estimation of diffusion processes from partial and
noisy observations. This is based on a convergent approximation to the first
two conditional moments of the innovation process through approximate
continuous-discrete filters of minimum variance. It is shown that, for finite
samples, the resulting approximate estimators converge to the exact one when
the error of the approximate filters decreases. For an increasing number of
observations, the estimators are asymptotically normal distributed and their
bias decreases when the above 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
partial and noisy observations distant in time.
