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

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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.

Suggested Citation

  • Donald W.K. Andrews, 1984. "A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model," Cowles Foundation Discussion Papers 734R, Cowles Foundation for Research in Economics, Yale University, revised Aug 1985.
    • Handle: RePEc:cwl:cwldpp:734r
    Note: CFP 658.
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    1. Engle, Robert F, 1974. "Band Spectrum Regression," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 15(1), pages 1-11, February.
    2. Maddala, G S, 1971. "The Use of Variance Components Models in Pooling Cross Section and Time Series Data," Econometrica, Econometric Society, vol. 39(2), pages 341-358, March.
    3. Amemiya, Takeshi, 1973. "Generalized Least Squares with an Estimated Autocovariance Matrix," Econometrica, Econometric Society, vol. 41(4), pages 723-732, July.
    4. Magnus, Jan R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Journal of Econometrics, Elsevier, vol. 7(3), pages 281-312, April.
    5. Beach, Charles M & MacKinnon, James G, 1978. "A Maximum Likelihood Procedure for Regression with Autocorrelated Errors," Econometrica, Econometric Society, vol. 46(1), pages 51-58, January.
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    2. Franco Peracchi, 1988. "Robust Estimators of Regression," UCLA Economics Working Papers 476, UCLA Department of Economics.
    3. Blackburn, McKinley L., 1997. "Misspecified skedastic functions in grouped-data models," Economics Letters, Elsevier, vol. 55(1), pages 1-8, August.

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