TY - JOUR

T1 - Particle approximations of the score and observed information matrix for parameter estimation in state space models with linear computational cost

AU - Nemeth, Christopher

AU - Fearnhead, Paul

AU - Mihaylova, Lyudmila Stoyanova

N1 - 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

PY - 2016/11

Y1 - 2016/11

N2 - 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.

AB - 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.

KW - Gradient ascent algorithm

KW - Maximum likelihood parameter estimation

KW - Particle filtering

KW - Sequential Monte Carlo

KW - Stochastic approximation

U2 - 10.1080/10618600.2015.1093492

DO - 10.1080/10618600.2015.1093492

M3 - Journal article

VL - 25

SP - 1138

EP - 1157

JO - Journal of Computational and Graphical Statistics

JF - Journal of Computational and Graphical Statistics

SN - 1061-8600

IS - 4

ER -