Un teorema di rappresentazione per lo stimatore vincolato

Abstract

A recent result in partitioned inversion (Faliva and Zoia, 2000) paves the way to shed some more light on constrained estimation, as the paper shows for the linear model. Indeed, a novel closed-form expression for the restricted least-squares(RLS) estimator is derived, which reads as a mirror image of the well-known Theil's(1961) solution and actually turns out to cover the latter as a special case. This leads eventually to an elegant representation theorem for the RLS estimator which combines classical and new results as well.