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

TL;DR

This paper presents a novel particle-based method for estimating the score and observed information matrix in state space models with linear computational cost, improving efficiency and robustness over previous quadratic-cost approaches.

Contribution

It introduces a new approach combining kernel density estimation and Rao-Blackwellisation to achieve linear computational cost and robustness in estimating key quantities for parameter inference.

Findings

Method reduces computational cost from quadratic to linear.

Estimates are robust to bandwidth choices in kernel density estimation.

Empirical results show improved parameter estimation accuracy.

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.