A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model
AbstractThis 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.
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Bibliographic InfoPaper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 734R.
Length: 30 pages
Date of creation: Dec 1984
Date of revision: Aug 1985
Publication status: Published in Econometrica (May 1985), 54(3): 687-698
Note: CFP 658.
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Other versions of this item:
- Andrews, Donald W K, 1986. "A Note on the Unbiasedness of Feasible GLS, Quasi-maximum Likelihood, Robust, Adaptive, and Spectral Estimators of the Linear Model," Econometrica, Econometric Society, vol. 54(3), pages 687-98, May.
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- Franco Peracchi, 1988. "Robust Estimators of Regression," UCLA Economics Working Papers 476, UCLA Department of Economics.
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