A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model

Donald Andrews ()

No 734R, Cowles Foundation Discussion Papers from Cowles Foundation for Research in Economics, Yale University

Abstract: This note presents a set of conditions on the defining functions of regression parameter estimators of the linear model. These conditions guarantee that the estimators are symmetrically distributed about the true parameter value, and hence are median unbiased, provided the conditional distribution of the vector of errors is symmetric given the matrix of regressors. The symmetry result holds even if the regression parameters are subject to linear restrictions. If the estimators posses one or more moments, then the symmetry result also implies mean unbiasedness. Similar conditions are provided that establish the property of origin (or shift) equivariance for the estimators. Common feasible GLS, quasi-ML, robust, adaptive, and spectral estimators are seen easily to satisfy the requisite conditions.

Keywords: Unbiasedness; linear model; parameter estimators (search for similar items in EconPapers)
Pages: 30 pages
Date: 1984-12, Revised 1985-08
Note: CFP 658.
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Published in Econometrica (May 1985), 54(3): 687-698

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Journal Article: A Note on the Unbiasedness of Feasible GLS, Quasi-maximum Likelihood, Robust, Adaptive, and Spectral Estimators of the Linear Model (1986)
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