Pötscher, Benedikt M. and Preinerstorfer, David (2022): A Modern GaussMarkov 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 GaussMarkov 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 published in Econometrica) either coincide with the classical theorems just mentioned, or contain extra assumptions that are alien to the GaussMarkov or Aitken Theorem.
Item Type:  MPRA Paper 

Original Title:  A Modern GaussMarkov Theorem? Really? 
Language:  English 
Keywords:  GaussMarkov 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:  118952 
Depositing User:  Benedikt Poetscher 
Date Deposited:  26 Oct 2023 05:27 
Last Modified:  26 Oct 2023 05:27 
References:  Gnot, S., Knautz, G., Trenkler, G. and Zmyslony, R. (1992). Nonlinear unbiased estimation in linear models. Statistics, 23 516. Halmos, P. R. (1946). The theory of unbiased estimation. Ann. Math. Statist., 17 3443. Hansen, B. E. (2021a). A modern GaussMarkov theorem, September 2021. Version accepted for publication in Econometrica. URL https://www.econometricsociety.org/system/files/192553.pdf. Hansen, B. E. (2021b). A modern GaussMarkov 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 GaussMarkov theorem. Econometrica, 90 12831294. 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 YorkLondonSydney. Kagan, A. M. and Salaevskii, O. (1969). The admissibility of leastsquares estimates is an exclusive property of the normal law. Mat. Zametki, 6 8189. 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 293309. Koopmann, R. (1982). Parameterschätzung bei a priori Information. Vandenhoeck & Ruprecht, Göttingen. Lehmann, E. L. and Casella, G. (1988). Theory of Point Estimation. 2nd ed. SpringerVerlag. Portnoy, S. (2022). Linearity of unbiased linear model estimators, American Statistician, 76 372375. Rosendal, C. (2009). Automatic continuity of group homomorphisms. The Bulletin of Symbolic Logic, 15 184214. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/118952 
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A Modern GaussMarkov Theorem? Really? (deposited 03 Apr 2022 19:15)

A Modern GaussMarkov Theorem? Really? (deposited 18 May 2022 16:14)

A Modern GaussMarkov Theorem? Really? (deposited 03 Jan 2023 07:03)
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A Modern GaussMarkov Theorem? Really? (deposited 03 Jan 2023 07:03)

A Modern GaussMarkov Theorem? Really? (deposited 18 May 2022 16:14)