New findings regarding parameter estimation in the Gauss-Markov model with restrictions on coefficients
Maria Grazia Zoia · Journal of Statistics and Management Systems · 2005
When addressing the issue of parameter estimation within a Gauss-Markov framework with linear constraints, several approaches are considered which turn out to hinge the solution of the problem on the inversion of an ad hoc bordered matrix. Within this connection, in the wake of a recent author’s result (Faliva and Zoia [3]), elegant partitioned inversion formulae — with projection operators as entries — are obtained, which lead to find informative closed-form expressions for the parameter estimator without collinearity qualification. This offers, on the one hand, enlightening solutions to the estimation problem, which covers Theil’s formula as a special case, and on the other, paves the way to gaining a deeper insight into linear estimator structure.