Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

Details Parameter Estimation for Hidden Markov Models with Intractable Likelihoods Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

2011-03-28

arxiv.org/abs/1103.5399v1

Mathematics

Statistics Theory

First version: 1 October 2010

Scientific paper

Approximate Bayesian computation (ABC) is a popular technique for approximating likelihoods and is often used in parameter estimation when the likelihood functions are analytically intractable. Although the use of ABC is widespread in many fields, there has been little investigation of the theoretical properties of the resulting estimators. In this paper we give a theoretical analysis of the asymptotic properties of ABC based maximum likelihood parameter estimation for hidden Markov models. In particular, we derive results analogous to those of consistency and asymptotic normality for standard maximum likelihood estimation. We also discuss how Sequential Monte Carlo methods provide a natural method for implementing likelihood based ABC procedures.

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