Seesaw method for combining parameter estimates

This paper introduces a "seesaw" scheme for parameter estimation where the overall parameter vector is divided into two parts. The estimate of the overall vector is formed by oscillating between the estimates for each of the two parts. A fundamental advantage of such a scheme is the preservation of potentially large investments in software while allowing for an extension of capability to include new vector for estimation. A specific case of interest involves cross-sectional data where there is interest in estimating the mean vector and covariance matrix of the initial state vector as well as certain parameters associated with the dynamics of the underlying differential equations (e.g., power spectral density parameters). This paper shows that under reasonable conditions the seesaw scheme will converge to the joint estimate for the full vector of unknown parameters.