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Time Series Analysis by State Space MethodsSecond Edition$
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James Durbin and Siem Jan Koopman

Print publication date: 2012

Print ISBN-13: 9780199641178

Published to Oxford Scholarship Online: December 2013

DOI: 10.1093/acprof:oso/9780199641178.001.0001

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Importance sampling for smoothing

Importance sampling for smoothing

Chapter:
(p.260) 11 Importance sampling for smoothing
Source:
Time Series Analysis by State Space Methods
Author(s):

J. Durbin

S.J. Koopman

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199641178.003.0011

This chapter develops the methodology of importance sampling based on simulation for the analysis of observations from the non-Gaussian and nonlinear models that were specified in Chapter 9. It shows that importance sampling methods can be adopted for estimating functions of the state vector and the error variance matrices of the resulting estimates. It develops estimates of conditional densities, distribution functions, and quantiles of interest. Of key importance is the method of estimating unknown parameters by maximum likelihood. The methods are based on standard ideas in simulation methodology and, in particular, importance sampling.

Keywords:   non-Gaussian models, nonlinear models, linear Gaussian model, importance density, maximum likelihood

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