Parameter Estimation for Hidden Markov Models with Intractable Likelihoods

TL;DR

This paper provides a theoretical analysis of the asymptotic properties of ABC-based maximum likelihood estimation for hidden Markov models, including consistency and normality, and discusses the use of Sequential Monte Carlo methods for implementation.

Contribution

It offers the first theoretical insights into the properties of ABC estimators for hidden Markov models and connects these methods with Sequential Monte Carlo techniques.

Findings

Establishes consistency of ABC-based estimators for HMMs.

Proves asymptotic normality of the estimators.

Highlights the role of Sequential Monte Carlo in implementing ABC procedures.

Abstract

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.