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Nemeth, C., Fearnhead, P. and Mihaylova, L.S. (Accepted: 2015) Particle Approximations of the Score and Observed Information Matrix for Parameter Estimation in State Space Models With Linear Computational Cost. Journal of Computational and Graphical Statistics. ISSN 1061-8600
Abstract
Poyiadjis et al. (2011) show how particle methods can be used to estimate both the score and the observed information matrix for state space models. These meth- ods either su er from a computational cost that is quadratic in the number of particles, or produce estimates whose variance increases quadratically with the amount of data. This paper introduces an alternative approach for estimating these terms at a computational cost that is linear in the number of particles. The method is derived using a combination of kernel density estimation to avoid the particle degeneracy that causes the quadratically increasing variance, and Rao-Blackwellisation. Crucially, we show the method is robust to the choice of bandwidth within the kernel density estimation, as it has good asymptotic properties regardless of this choice. Our estimates of the score and observed information matrix can be used within both online and batch procedures for estimating parameters for state space models. Empirical results show improved parameter estimates compared to existing methods at a signi cantly reduced computational cost.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2015 Taylor & Francis. This is an author produced version of a paper subsequently published in Journal of Computational and Graphical Statistics. Uploaded in accordance with the publisher's self-archiving policy. |
Keywords: | Gradient ascent algorithm; Maximum likelihood parameter estimation; Particle filtering; Sequential Monte Carlo; Stochastic approximation |
Dates: |
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Institution: | The University of Sheffield |
Academic Units: | The University of Sheffield > Faculty of Engineering (Sheffield) > Department of Automatic Control and Systems Engineering (Sheffield) |
Depositing User: | Symplectic Sheffield |
Date Deposited: | 21 Jan 2016 11:14 |
Last Modified: | 24 Apr 2017 00:24 |
Published Version: | http://dx.doi.org/10.1080/10618600.2015.1093492 |
Status: | Published |
Publisher: | Taylor & Francis |
Refereed: | Yes |
Identification Number: | 10.1080/10618600.2015.1093492 |
Related URLs: | |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:92279 |
Available Versions of this Item
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Particle Approximations of the Score and Observed Information Matrix for Parameter Estimation in State Space Models With Linear Computational Cost. (deposited 05 Feb 2015 11:07)
- Particle Approximations of the Score and Observed Information Matrix for Parameter Estimation in State Space Models With Linear Computational Cost. (deposited 21 Jan 2016 11:14) [Currently Displayed]