Pötscher, Benedikt M. and Preinerstorfer, David (2022): A Modern Gauss-Markov Theorem? Really?
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Abstract
We show that the theorems in Hansen (2021a) (the version accepted by Econometrica), except for one, are not new as they coincide with classical theorems like the good old Gauss-Markov or Aitken Theorem, respectively; the exceptional theorem is incorrect. Hansen (2021b)corrects this theorem. As a result, all theorems in the latter version coincide with the above mentioned classical theorems. Furthermore, we also show that the theorems in Hansen (2022)(the version forthcoming in Econometrica) either coincide with the classical theorems just mentioned, or contain extra assumptions that are alien to the Gauss-Markov or Aitken Theorem.
Item Type: | MPRA Paper |
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Original Title: | A Modern Gauss-Markov Theorem? Really? |
Language: | English |
Keywords: | Gauss-Markov Theorem, Aitken Theorem, unbiased estimation |
Subjects: | C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C20 - General |
Item ID: | 112607 |
Depositing User: | Benedikt Poetscher |
Date Deposited: | 03 Apr 2022 19:15 |
Last Modified: | 03 Apr 2022 19:15 |
References: | Gnot, S., Knautz, G., Trenkler, G. and Zmyslony, R. (1992). Nonlinear unbiased estimation in linear models. Statistics, 23 5-16. Halmos, P. R. (1946). The theory of unbiased estimation. Ann. Math. Statist., 17 34-43. Hansen, B. E. (2021a). A modern Gauss-Markov theorem, September 2021. Version accepted for publication in Econometrica. URL https://www.econometricsociety.org/system/files/19255-3.pdf. Hansen, B. E. (2021b). A modern Gauss-Markov theorem, December 2021. Update of September 2021 version accepted for publication in Econometrica. URL https://www.ssc.wisc.edu/~bhansen/papers/gauss.pdf. Hansen, B. E. (2021c). Econometrics. Princeton University Press, forthcoming. Version August 18, 2021. Hansen, B. E. (2022). A modern Gauss-Markov theorem. Version forthcoming in Econometrica. URL https://www.ssc.wisc.edu/~bhansen/papers/gauss2.pdf. Kagan, A. M., Linnik, Y. V. and Rao, C. R. (1973). Characterization problems in mathematical statistics. Wiley Series in Probability and Mathematical Statistics, John Wiley & Sons, New York-London-Sydney. Kagan, A. M. and Salaevskii, O. (1969). The admissibility of least-squares estimates is an exclusive property of the normal law. Mat. Zametki, 6 81-89. Knautz, H. (1993). Nichtlineare Schätzung des Parametervektors im linearen Regressionsmodell, vol. 133 of Mathematical Systems in Economics. Verlag Anton Hain, Frankfurt am Main. Knautz, H. (1999). Nonlinear unbiased estimation in the linear regression model with nonnormal disturbances. J. Statist. Plann. Inference, 81 293-309. Koopmann, R. (1982). Parameterschätzung bei a priori Information. Vandenhoeck & Ruprecht, Göttingen. Lehmann, E. L. and Casella, G. (1988). Theory of Point Estimation. 2nd ed. Springer-Verlag. Portnoy, S. (2022). Linearity of unbiased linear model estimators, February 26, 2022. Rosendal, C. (2009). Automatic continuity of group homomorphisms. The Bulletin of Symbolic Logic, 15 184-214. |
URI: | https://mpra.ub.uni-muenchen.de/id/eprint/112607 |
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