The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator |
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| Authors: | Simo Puntanen George P H Styan |
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| Institution: | 1. Department of Mathematical Sciences , University of Tampere , P.O. Box 607, SF-33101, Tampere , Finland;2. Department of Mathematics and Statistics , McGill University , 805 Ouest, Rue Sherbrooke, Montréal, Québec , H3A 2K6 , Canada |
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| Abstract: | It is well known that the ordinary least squares estimator of Xβ in the general linear model E y = Xβ, cov y = σ2 V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverses and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided. |
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| Keywords: | Canonical correlation Generalized inverse Hat matrix McElroy's condition Orthogonal projector Weighted least squares |
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