Diffuse Restricted Kalman Filtering
ADRIAN HERINGER PIZZINGA · Communication in Statistics- Theory and Methods · 2013
This article investigates how the use of an initial diffuse state vector affects the use of the Kalman smoother under linear restrictions. The contribution is twofold. First, using elementary linear and matrix algebra, it is established that it is still possible to obtain restricted smoothed state vectors in the “diffuse” period under quite general conditions. Second, using results from general conditional expectation theory, it is proven that the extension of the restricted Kalman smoother also preserves conditional statistical efficiency, given some meaningful information sets.