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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.

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File URL: http://cowles.econ.yale.edu/P/cd/d07a/d0734-r.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 734R.

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Length: 30 pages
Date of creation: Dec 1984
Date of revision: Aug 1985
Publication status: Published in Econometrica (May 1985), 54(3): 687-698
Handle: RePEc:cwl:cwldpp:734r

Note: CFP 658.
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Postal: Cowles Foundation, Yale University, Box 208281, New Haven, CT 06520-8281 USA

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Keywords: Unbiasedness; linear model; parameter estimators;

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References

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  1. R. F. Engle, 1972. "Band Spectrum Regressions," Working papers 96, Massachusetts Institute of Technology (MIT), Department of Economics.
  2. Amemiya, Takeshi, 1973. "Generalized Least Squares with an Estimated Autocovariance Matrix," Econometrica, Econometric Society, vol. 41(4), pages 723-32, July.
  3. Magnus, J.R., 1978. "Maximum likelihood estimation of the GLS model with unknown parameters in the disturbance covariance matrix," Open Access publications from Tilburg University urn:nbn:nl:ui:12-153204, Tilburg University.
  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.
  6. 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.
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Cited by:
  1. Blackburn, McKinley L., 1997. "Misspecified skedastic functions in grouped-data models," Economics Letters, Elsevier, vol. 55(1), pages 1-8, August.
  2. Franco Peracchi, 1988. "Robust Estimators of Regression," UCLA Economics Working Papers 476, UCLA Department of Economics.

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