Abstract
In this extract from the second supplement of his famous Théorie analytique des probabilités, Laplace makes, in the context of simple linear regression, a large-sample comparison of what we now call L 1- and L 2- estimation. He essentially introduces the notion of asymptotic relative efficiency and, incidentally, pioneers the theory of order statistics.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
Eisenhart, C. (1961). Boscovich and the combination of observations. In: Roger Joseph Boscovich, L.L. Whyte, ed. Allen and Unwin, London, pp. 200–212. [Reprinted in Kendall and Plackett (1977), pp. 88–100.]
Fisher, R.A. (1920). A mathematical examination of the methods of determining the accuracy of an observation by the mean error, and by the mean square error. Mon. Nat. R. Astron. Soc., 80, 758–770. [Reprinted as Paper 2 in Fisher (1950).]
Fisher, R. A. (1950). Contributions to Mathematical Statistics. Wiley, New York.
Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. Wiley, New York.
Kendall, M. G. and Plackett, R. L. (eds.) (1977) Studies in the History of Statistics and Probability. Vol. 2. Griffin, London.
Laplace, P.S. (1793). Sur quelques points du système du monde. Mém. Acad. R. Sci. Paris (1789), 1–87. [Reprinted in Oeuvres de Laplace, 11. Imprimerie Royale, Paris (1847).]
Laplace, P.S. (1799). Traité de mécanique céleste, Vol. 2, 3rd Book, Sections 40–41. [Translated into English by N. Bowditch in 1832 and reprinted in Laplace (1966, pp. 434–442, 448–450) .]
Laplace, P.S. (1810). Mémoire sur les approximations des formules qui sont fonctions de trés grands nombres et sur leur application aux probabilités. Mém. Acad. R. Sci. Paris, 353–415. [Reprinted in Oeuvres de Laplace, 12. Imprimerie Royale, Paris (1847).]
Laplace, P.S. (1812). Théorie analytique des probabilités. Courier, Paris. [Reprinted in Oeuvres de Laplace, 7. Imprimerie Royale, Paris (1847).]
Laplace, P.S. (1818). Théorie analytique des probabilités, deuxième sup-plément. [Reprinted in Oeuvres de Laplace, 7. Imprimerie Royale, Paris (1847).]
Laplace, P. S. (1966). Celestial Mechanics, Vol. 2, translated, with commenaty, by N. Bodwitch. Chelsea, New York.
Legendre, A.M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Courier, Paris. [Reprinted by Dover, New York, 1959.]
Sheynin, O.B. (1973). R.J. Boscovich’s work on probability. Arch. Hist. Exact Sci., 9, 306–324.
Stigler, S.M. (1973). Laplace, Fisher, and the discovery of the concept of sufficiency. Biometrika, 60, 439–445. [Reprinted in Kendall and Plackett (1977), pp. 271–277.]
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
David, H.A., Edwards, A.W.F. (2001). The Introduction of Asymptotic Relative Efficiency. In: Annotated Readings in the History of Statistics. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3500-0_9
Download citation
DOI: https://doi.org/10.1007/978-1-4757-3500-0_9
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4419-3174-0
Online ISBN: 978-1-4757-3500-0
eBook Packages: Springer Book Archive