On Multi-Step MLE-Process for Ergodic Diffusion

Abstract: We propose a new method of the construction of the asymptotically efficient estimator-processes asymptotically equivalent to the MLE and the same time much more easy to calculate. We suppose that the observed process is ergodic diffusion and that there is a learning time interval of the length negligeable with respect to the whole time of observations. The preliminary estimator obtained after the learning time is then used in the construction of one-step and two-step MLE processes. We discuss the possibility of the applications of the proposed estimation procedure to several other observations models.