Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

摘要

Approximate Bayesian computation (ABC) is a popular technique forapproximating likelihoods and is often used in parameter estimation when thelikelihood functions are analytically intractable. Although the use of ABC iswidespread in many fields, there has been little investigation of thetheoretical properties of the resulting estimators. In this paper we give atheoretical analysis of the asymptotic properties of ABC based maximumlikelihood parameter estimation for hidden Markov models. In particular, wederive results analogous to those of consistency and asymptotic normality forstandard maximum likelihood estimation. We also discuss how Sequential MonteCarlo methods provide a natural method for implementing likelihood based ABCprocedures.