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Biometrika 1999 86(1):183-190; doi:10.1093/biomet/86.1.183
© 1999 by Biometrika Trust
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Assessing the predictive influence of cases in a state space process

JE CavanaughA1 and WO JohnsonA2

A1 Department of Statistics, 222 Mathematical Sciences Building, University of Missouri, Columbia, Missouri 65211, USA cavanaugh@stat.missouri.edu A2 Division of Statistics, University of California, Davis, CA 95616, USA wojohnson@ucdavis.edu

An important inferential objective in state space modelling is to recover unobserved states using fixed-interval smoothing. Thus, the identification of cases which have a substantial influence on the smoothers is a relevant practical problem. To facilitate this identification, we propose a case-deletion diagnostic which can be easily computed using the outputs of the standard filtering and smoothing algorithms. Our diagnostic is defined as the Kullback-Leibler directed divergence between two versions of the conditional density which determines the smoothers, one based on all the data, the other based on all the data except for the case or cases in question. We investigate the detection performance of the diagnostic in a practical application.

Keywords:Case-deletion diagnostic; EM algorithm; Fixed-interval smoothing; Kalman filtering; Kullback-Leibler divergence; Prediction; Predictive influence function; State space modelling; Time series analysis.


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