Optimality of the least squares estimator

Robert Berk and Jiunn T. Hwang

Journal of Multivariate Analysis, 1989, vol. 30, issue 2, 245-254

Abstract: In a standard linear model, we explore the optimality of the least squares estimator under assuptions stronger than those for the Gauss-Markov theorem. The conclusion is then much stronger than that of the Gauss-Markov theorem. Specifically, two results are cited below: Under the assumption that the unobserved error [var epsilon] has a spherically symmetric distribution, the least squares estimator for the regression coefficient [beta] is shown to maximize the probability that [beta] - [beta] stays in any symmetric convex set among linear unbiased estimators [beta]. With the additional assumption that [var epsilon] is unimodal, the conclusion holds among equivariant estimators. The import of these results for risk functions is also discussed.

Keywords: Gauss-Markov; Theorem; unbiased; estimator; [beta]; spherically; symmetric; distribution (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (3)

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