Using a priori data to refine parameter estimates (Q1111519)

A procedure is proposed for considering a priori data that for a parameter being estimated the true value is a member of some set. This procedure is contained in projecting estimates of the least squares for an a priori set. We prove that in many cases, when the true value lies on the boundary, a uniform increase in estimation accuracy that is independent of the number of observations occurs. The procedure is used to obtain refined estimates for symmetric and nonnegative definite matrices.