Score and Observed Information Matrix Estimation in State-Space Models Using Sequential Monte Carlo

• Activity Number: 417
• Type: Topic Contributed
• Date/Time: Tuesday, August 6, 2013 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Computing
• Author(s): Pierre Etienne Jacob*+ and Arnaud Doucet and Sylvain Rubenthaler
• Companies: National University of Singapore and University of Oxford and CNRS Nice
• Keywords: Sequential Monte Carlo ; State-Space Model ; Hidden Markov Model ; Score vector ; Information Matrix ; Smoothing

Abstract

Iterated Filtering has recently been introduced as an original approach to perform maximum likelihood parameter estimation in general state-space models where it is possible to simulate the latent Markov model but impossible to evaluate its transition density. It relies on an approximation of the score vector for general statistical models based on an artificial posterior distribution which does not require the analytical calculation of any derivative. Building upon this insightful work, we propose alternative estimates of the score vector and extend the method to "derivative-free" estimates of the Observed Information Matrix. Interestingly the proposed method relies on "smoothing" estimates instead of the "filtering" estimates in the original iterated filtering method.