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Biometrika 1989 76(1):65-79; doi:10.1093/biomet/76.1.65
© 1989 by Biometrika Trust
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A fast algorithm for signal extraction, influence and cross-validation in state space models

ROBERT KOHN and CRAIG F. ANSLEY

Australian Graduate School of Management, University of New South Wales Kensington, N. S. W. 2033, Australia

A fast algorithm is developed for computing the conditional mean and variance of the signal given the observations in a signal plus noise model. The resulting recursions can be applied immediately to provide new and efficient formulae for smoothing part or all of the state vector. The ideas of studentized residuals and leverage from regression analysis are generalized to state space models, and the new algorithm is used to compute the various measures. The results are also applied to obtain a new efficient algorithm for polynomial spline smoothing.

Key Words: Bayes estimate • Cross-validation • Generalized cross-validation • Leverage • Signal extraction • Spline smoothing • Studentized residual


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