On the calculation of minimum variance estimators for unobservable dependent variables

The determination of minimum variance estimators in an unusual context is considered. The problem arises from an attempt to perform a regression with an unobservable dependent variable. The required minimum variance estimator is shown to satisfy a linear system of equations where the coefficient matrix has a simple structure. Uniqueness of the estimator is established by determining necessary and sufficient conditions on the data which guarantee positive definiteness of this coefficient matrix. Numerical aspects of the method of computation are also briefly explored