On Multi-Step MLE-Process for Ergodic Diffusion

TL;DR

This paper introduces a new, computationally simpler method for constructing asymptotically efficient estimators for ergodic diffusion processes, leveraging preliminary estimates and multi-step procedures.

Contribution

It proposes a novel multi-step MLE-process that is asymptotically equivalent to the traditional MLE but easier to compute, applicable to ergodic diffusion models.

Findings

The method achieves asymptotic efficiency.

It simplifies the calculation of estimators.

Applicable to various observation models.

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.