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Particle filters for partially observed diffusions

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  • Paul Fearnhead
  • Omiros Papaspiliopoulos
  • Gareth O. Roberts

Abstract

We introduce a novel particle filter scheme for a class of partially observed multivariate diffusions. We consider a variety of observation schemes, including diffusion observed with error, observation of a subset of the components of the multivariate diffusion and arrival times of a Poisson process whose intensity is a known function of the diffusion (Cox process). Unlike currently available methods, our particle filters do not require approximations of the transition and/or the observation density by using time discretizations. Instead, they build on recent methodology for the exact simulation of the diffusion process and the unbiased estimation of the transition density. We introduce the generalized Poisson estimator, which generalizes the Poisson estimator of Beskos and co-workers. A central limit theorem is given for our particle filter scheme. Copyright (c) 2008 Royal Statistical Society.

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Bibliographic Info

Article provided by Royal Statistical Society in its journal Journal of the Royal Statistical Society: Series B (Statistical Methodology).

Volume (Year): 70 (2008)
Issue (Month): 4 ()
Pages: 755-777

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Handle: RePEc:bla:jorssb:v:70:y:2008:i:4:p:755-777

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Cited by:
  1. Stefano Iacus & Masayuki Uchida & Nakahiro Yoshida, 2006. "Parametric estimation for partially hidden diffusion processes sampled at discrete times," UNIMI - Research Papers in Economics, Business, and Statistics unimi-1042, Universitá degli Studi di Milano.
  2. Konstantinos Kalogeropoulos & Gareth O. Roberts & Petros Dellaportas, 2007. "Inference for stochastic volatility models using time change transformations," Papers 0711.1594, arXiv.org.
  3. Hermann Singer, 2011. "Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms," AStA Advances in Statistical Analysis, Springer, vol. 95(4), pages 375-413, December.
  4. Mark Briers & Arnaud Doucet & Simon Maskell, 2010. "Smoothing algorithms for state–space models," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(1), pages 61-89, February.

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