Filtering via estimating functions Original Research Article

A result of Godambe [1] on optimal combination of estimating functions for discrete time stochastic processes is extended to discrete time state space models and to continuous time counting process models. The extensions so obtained may be applicable in a wider context than the standard notions based upon the conditional mean. It is shown that a number of results in the literature are special cases. The theory is applied to obtain recursive estimates for continuous time counting processes. Optimal linear combination of estimating functions can shed light on the form of recursion satisfied by the usual filter, namely conditional expectation of the unobserved underlying process given the observation history.