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Biometrika 1994 81(2):390-395; doi:10.1093/biomet/81.2.390
© 1994 by Biometrika Trust
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MISCELLANEA

Bayesian Kalman filtering with elliptically contoured errors

F. J. GIRON and J. C. ROJANO

Departamento de Estadistica, Universidad de Málaga 29071-Málaga, Spain

The basic recursive equations of the Kalman filter, for independent normally distributed error sources in both the observation and the system equations, are shown to hold for a larger class of distributions. It is shown that, for error sources following jointly a general elliptical distribution, the conditional posterior distribution of the parameters and the one-step ahead predictive distribution at every stage t are also elliptical. This generalizes some recent results of Meinhold & Singpurwalla for error sources distributed as multivariate Student t and some older results of Zellner for the linear regression model.

Key Words: Elliptical distribution • Kalman filter • Posterior distribution • Predictive distribution • Scale mixture • Weak robustness


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