Smoothing Estimation of Stochastic Processes: Change of Initial Condition Formulas,
WISCONSIN UNIV-MADISON MATHEMATICS RESEARCH CENTER
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By posing the change of initial condition CIC problem in the theory of smoothing in linear estimation in a setting stripped of all inessentials, simple, insightful derivations of most CIC formulas and a new likelihood formula are provided. Specifically, the CIC or partitioning problem is one of low rank perturbation to a covariance kernel and the formulas are simple consequences of inversion formulas for fixed rank modification of a positive definite kernel or matrix. The present derivation basically handles the discrete, continuous-discrete, and continuous cases at once previous derivations had treated the discrete and continuous separately. The continuous- discrete results are new. Originator-supplied key words include Linear estimation, Smoothing, Filtering, Covariance kernel, Hilbert space.
- Statistics and Probability