On oblique projectors

Oblique projectors are useful in many contexts, especially in the instrumen tal variable estimation in regression models in econometrics, where the dis turbance term tends to be correlated with predictor variables. This paper a ddresses two important questions regarding oblique projectors: (1) products of two oblique projectors and (2) decompositions of oblique projectors, In (1), we investigate what determines the onto- and the along-spaces of an o blique projector defined as a product of two oblique projectors under a var iety of conditions. In (2), we examine various decompositions of oblique pr ojectors when both predictor variables and instrumental variables consist o f two distinct sets of variables. These decompositions are analogous to tho se of orthogonal projectors. (C) 1999 Elsevier Science Inc. All rights rese rved. AMS classification: 15A03; 15A09.