Improvements on Parameter Estimation based on Particle Approximations of the Gradient and Information Matrix in State Space Models

Abstract

Let (Xt , Yt )t≥1 be a homogeneous discrete-time bivariate stochastic process where (Xt )t≥1 is a Markov chain and (Yt |Xt )t≥1 is a conditionally independent sequence such that each Yt is determined almost surely by Xt . If we also assume that only (Yt )t≥1 is available for inference, i.e. that the Markov chain (Xt )t≥1 is unobservable, then (Xt , Yt )t≥1 is usually called a state space or hidden Markov model (HMM). Usually, the law of (Xt , Yt )t≥1 is also taken to be indexed by a d-dimensional parameter θ taking values in Θ.