Unbiased Parameter Estimation for Partially Observed Diffusions

TL;DR

This paper introduces a novel double randomization scheme to unbiasedly estimate static parameters in partially observed diffusion processes, eliminating time discretization bias and outperforming existing methods in numerical experiments.

Contribution

It develops a new unbiased estimation method for static parameters in partially observed diffusions using Markovian stochastic approximation, removing discretization bias.

Findings

Estimator is proven to be unbiased.

Method empirically outperforms existing unbiased techniques.

Numerical examples demonstrate practical effectiveness.

Abstract

In this article we consider the estimation of static parameters for partially observed diffusion process with discrete-time observations over a fixed time interval. In particular, we assume that one must time-discretize the partially observed diffusion process and work with the model with bias and consider maximizing the resulting log-likelihood. Using a novel double randomization scheme, based upon Markovian stochastic approximation we develop a new method to unbiasedly estimate the static parameters, that is, to obtain the maximum likelihood estimator with no time discretization bias. Under assumptions we prove that our estimator is unbiased and investigate the method in several numerical examples, showing that it can empirically out-perform existing unbiased methodology.