Journal
ELECTRONIC JOURNAL OF STATISTICS
Volume 5, Issue -, Pages 1090-1122Publisher
INST MATHEMATICAL STATISTICS
DOI: 10.1214/11-EJS632
Keywords
Auxiliary particle filter; EM algorithm; exact algorithm; generalised Poisson estimator; partially observed diffusion process; sequential Monte Carlo
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This paper concerns the use of the expectation-maximisation (EM) algorithm for inference in partially observed diffusion processes. In this context, a well known problem is that all except a few diffusion processes lack closed-form expressions of the transition densities. Thus, in order to estimate efficiently the EM intermediate quantity we construct, using novel techniques for unbiased estimation of diffusion transition densities, a random weight fixed-lag auxiliary particle smoother, which avoids the well known problem of particle trajectory degeneracy in the smoothing mode. The estimator is justified theoretically and demonstrated on a simulated example.
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