A Note on the Unbiasedness of Feasible GLS, Quasi-Maximum Likelihood, Robust Adaptive, and Spectral Estimators of the Linear Model
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.
|Date of creation:||Dec 1984|
|Date of revision:||Aug 1985|
|Publication status:||Published in Econometrica (May 1985), 54(3): 687-698|
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- R. F. Engle, 1972.
"Band Spectrum Regressions,"
96, Massachusetts Institute of Technology (MIT), Department of Economics.
- 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 341-58, March.
- 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.
- Amemiya, Takeshi, 1973. "Generalized Least Squares with an Estimated Autocovariance Matrix," Econometrica, Econometric Society, vol. 41(4), pages 723-32, July.
- 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.
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