Theory of segmented particle filters.(English)Zbl 1338.65023

Summary: We study the asymptotic behavior of a new particle filter approach for the estimation of hidden Markov models. In particular, we develop an algorithm where the latent-state sequence is segmented into multiple shorter portions, with an estimation technique based upon a separate particle filter in each portion. The partitioning facilitates the use of parallel processing, which reduces the wall-clock computational time. Based upon this approach, we introduce new estimators of the latent states and likelihood which have similar or better variance properties compared to estimators derived from standard particle filters. We show that the likelihood function estimator is unbiased, and show asymptotic normality of the underlying estimators.

MSC:

 65C60 Computational problems in statistics (MSC2010) 62M05 Markov processes: estimation; hidden Markov models 62M20 Inference from stochastic processes and prediction 65C05 Monte Carlo methods 65Y05 Parallel numerical computation
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