Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost

Nemeth, Christopher and Fearnhead, Paul and Mihaylova, Lyudmila Stoyanova (2016) 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, 25 (4). pp. 1138-1157. ISSN 1061-8600

[thumbnail of Particle_Approximations_of_the_Score_and_Observed_Information_Matrix_for_Parameter_Estimation_in_State_Space_Models_With_Linear_Computational_Cost]
Preview
PDF (Particle_Approximations_of_the_Score_and_Observed_Information_Matrix_for_Parameter_Estimation_in_State_Space_Models_With_Linear_Computational_Cost)
Particle_Approximations_of_the_Score_and_Observed_Information_Matrix_for_Parameter_Estimation_in_State_Space_Models_With_Linear_Computational_Cost.pdf - Accepted Version
Available under License Creative Commons Attribution.

Download (4MB)

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 methods either suffer 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 significantly reduced computational cost. Supplementary materials including code are available.

Item Type:
Journal Article
Journal or Publication Title:
Journal of Computational and Graphical Statistics
Additional Information:
This is an Accepted Manuscript of an article published by Taylor & Francis Group in Journal of Computational and Graphical Statistics on 22/10/2015, available online:http://www.tandfonline.com/10.1080/10618600.2015.1093492
Uncontrolled Keywords:
/dk/atira/pure/subjectarea/asjc/2600/2607
Subjects:
?? gradient ascent algorithmmaximum likelihood parameter estimationparticle filteringsequential monte carlostochastic approximationdiscrete mathematics and combinatoricsstatistics and probabilitystatistics, probability and uncertainty ??
ID Code:
76835
Deposited By:
Deposited On:
24 Nov 2015 13:04
Refereed?:
Yes
Published?:
Published
Last Modified:
31 Dec 2023 00:37