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

Uriel M. Silva, Rodolfo Santos Nunes Rodrigues, Felipe Carvalho Álvares da Silva, Luiz Henrique Duczmal, Denise Burgarelli Duczmal


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.

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