The Introduction of Asymptotic Relative Efficiency

Comments on Laplace (1818)
  • H. A. David
  • A. W. F. Edwards
Part of the Springer Series in Statistics book series (SSS)


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.


Order Statistic Asymptotic Distribution Advantageous Method Joint Density Asymptotic Relative Efficiency 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 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.]Google Scholar
  2. 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).]Google Scholar
  3. Fisher, R. A. (1950). Contributions to Mathematical Statistics. Wiley, New York.zbMATHGoogle Scholar
  4. Hald, A. (1998). A History of Mathematical Statistics from 1750 to 1930. Wiley, New York.zbMATHGoogle Scholar
  5. Kendall, M. G. and Plackett, R. L. (eds.) (1977) Studies in the History of Statistics and Probability. Vol. 2. Griffin, London.zbMATHGoogle Scholar
  6. 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).]Google Scholar
  7. 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) .]Google Scholar
  8. 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).]Google Scholar
  9. Laplace, P.S. (1812). Théorie analytique des probabilités. Courier, Paris. [Reprinted in Oeuvres de Laplace, 7. Imprimerie Royale, Paris (1847).]Google Scholar
  10. Laplace, P.S. (1818). Théorie analytique des probabilités, deuxième sup-plément. [Reprinted in Oeuvres de Laplace, 7. Imprimerie Royale, Paris (1847).]Google Scholar
  11. Laplace, P. S. (1966). Celestial Mechanics, Vol. 2, translated, with commenaty, by N. Bodwitch. Chelsea, New York.Google Scholar
  12. Legendre, A.M. (1805). Nouvelles méthodes pour la détermination des orbites des comètes. Courier, Paris. [Reprinted by Dover, New York, 1959.]Google Scholar
  13. Sheynin, O.B. (1973). R.J. Boscovich’s work on probability. Arch. Hist. Exact Sci., 9, 306–324.zbMATHGoogle Scholar
  14. 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.]MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2001

Authors and Affiliations

  • H. A. David
    • 1
  • A. W. F. Edwards
    • 2
  1. 1.Statistical Laboratory and Department of StatisticsIowa State UniversityAmesUSA
  2. 2.Gonville and Caius CollegeCambridgeUK

Personalised recommendations