A Modern Gauss-Markov Theorem? Really?

Pötscher, Benedikt M. and Preinerstorfer, David (2022): A Modern Gauss-Markov Theorem? Really?

Abstract

We show that the theorems in Hansen (2021b) (Econometrica, forthcoming) are not new as they coincide with classical theorems like the good old Gauss-Markov or Aitken Theorem, respectively.

• Item Type: MPRA Paper
• 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

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). Econometrics. Princeton University Press, forthcoming. Version August 18, 2021.

Hansen, B. E. (2021b). A modern Gauss-Markov theorem, December 2021. Forthcoming in Econometrica.

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.

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.

Rosendal, C. (2009). Automatic continuity of group homomorphisms. The Bulletin of Symbolic Logic, 15 184-214.