Exact filters for Newton-Raphson parameter estimation algorithms for continuous-time partially observed stochastic systems

Abstract

This paper presents explicit finite-dimensional filters for implementing Newton-Raphson (NR) parameter estimation algorithms. The models which exhibit nonlinear parameter dependence are stochastic, continuous-time and partially observed. The implementation of the NR algorithm requires evaluation of the log-likelihood gradient and the Fisher information matrix. Fisher information matrices are important in bounding the estimation error from below, via the Cramer-Rao bound. The derivations are based on relations between incomplete and complete data, likelihood, gradient and Hessian likelihood functions, which are derived using Girsanov's measure transformations.