Penalized likelihood smoothing in robust state space models |
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Authors: | Ludwig Fahrmeir Rita Künstler |
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Institution: | Institut für Statistik, Universit?t München, Ludwigsstr. 33, D-80539 München, Germany (e-mail: fahrmeir@stat.uni-muenchen.de), DE
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Abstract: | In likelihood-based approaches to robustify state space models, Gaussian error distributions are replaced by non-normal alternatives
with heavier tails. Robustified observation models are appropriate for time series with additive outliers, while state or
transition equations with heavy-tailed error distributions lead to filters and smoothers that can cope with structural changes
in trend or slope caused by innovations outliers. As a consequence, however, conditional filtering and smoothing densities
become analytically intractable. Various attempts have been made to deal with this problem, reaching from approximate conditional
mean type estimation to fully Bayesian analysis using MCMC simulation. In this article we consider penalized likelihood smoothers,
this means estimators which maximize penalized likelihoods or, equivalently, posterior densities. Filtering and smoothing
for additive and innovations outlier models can be carried out by computationally efficient Fisher scoring steps or iterative
Kalman-type filters. Special emphasis is on the Student family, for which EM-type algorithms to estimate unknown hyperparameters
are developed. Operational behaviour is illustrated by simulation experiments and by real data applications.
Received: March 1998 |
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Keywords: | : Additive outliers EM algorithm innovations outliers iterative Kalman Filtering non-Gaussian state space models |
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