论文信息 - Gauss on least-squares and maximum-likelihood estimation

Gauss on least-squares and maximum-likelihood estimation

Gauss’ 1809 discussion of least squares, which can be viewed as the beginning of mathematical statistics, is reviewed. The general consensus seems to be that Gauss’ arguments are at fault, but we show that his reasoning is in fact correct, given his self-imposed restrictions, and persuasive without these restrictions.

J. Magnus

[1] P. Gorroochurn. Classic Topics on the History of Modern Mathematical Statistics: From Laplace to More Recent Times , 2016 .

[2] Stephen M. Stigler,et al. The History of Statistics: The Measurement of Uncertainty before 1900 by Stephen M. Stigler (review) , 1986, Technology and Culture.

[3] D. Renn. The History of Statistics in the 17th and 18th Centuries: Against the Changing Background of Intellectual, Scientific and Religious Thought . By Karl Pearson [Charles Griffin, 1978] , 1979 .

[4] C. Gauss. Theory of the Motion of the Heavenly Bodies Moving About the Sun in Conic Sections , 1957 .

[5] G. Baxter. ON A CHARACTERIZATION OF THE NORMAL LAW. , 1955, Proceedings of the National Academy of Sciences of the United States of America.

[6] Carl Friedrich Gauss. Theoria motus corporum coelestium , 1981 .

[7] Karl Pearson,et al. The History of statistics in the 17th and 18th centuries against the changing background of intellectual, scientific, and religious thought : lectures by Karl Pearson given at University College, London, during the academic sessions, 1921-1933 , 1978 .

[8] Adrien-Marie Legendre,et al. Nouvelles méthodes pour la détermination des orbites des comètes , 1970 .

[9] K. F. Gauss,et al. Theoria combinationis observationum erroribus minimis obnoxiae , 1823 .