Efficient inference for nonlinear state space models: An automatic sample size selection rule

This paper studies the maximum likelihood estimation of nonlinear state space models. Particle Markov chain Monte Carlo method is introduced to implement the Monte Carlo expectation maximization algorithm for more accurate and robust estimation. Under this framework, an automated sample size selection criterion is constructed via renewal theory. This criterion would increase the sample size when the relative likelihood indicates that the parameters are close to each other. The proposed methodology is applied to the stochastic volatility model and another nonlinear state space model for illustration, where the results show better estimation performance.