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May 1999 On the history of maximum likelihood in relation to inverse probability and least squares
Anders Hald
Statist. Sci. 14(2): 214-222 (May 1999). DOI: 10.1214/ss/1009212248


It is shown that the method of maximum likelihood occurs in rudimentary forms before Fisher [Messenger of Mathematics 41 (1912) 155–160], but not under this name. Some of the estimates called “most probable” would today have been called “most likely.” Gauss [Z. Astronom. Verwandte Wiss. 1 (1816) 185–196] used invariance under parameter transformation when deriving his estimate of the standard deviation in the normal case. Hagen [Grundzüge der Wahrschein­lichkeits­Rechnung, Dümmler, Berlin (1837)] used the maximum likelihood argument for deriving the frequentist version of the method of least squares for the linear normal model. Edgeworth [J. Roy. Statist. Soc. 72 (1909) 81–90] proved the asymptotic normality and optimality of the maximum likelihood estimate for a restricted class of distributions. Fisher had two aversions: noninvariance and unbiasedness. Replacing the posterior mode by the maximum likelihood estimate he achieved invariance, and using a two­stage method of maximum likelihood he avoided appealing to unbiasedness for the linear normal model.


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Anders Hald. "On the history of maximum likelihood in relation to inverse probability and least squares." Statist. Sci. 14 (2) 214 - 222, May 1999.


Published: May 1999
First available in Project Euclid: 24 December 2001

zbMATH: 1059.62502
MathSciNet: MR1722061
Digital Object Identifier: 10.1214/ss/1009212248

Keywords: Chauvenet , confidence limits , credible limits , Edgeworth , Encke , Fisher , Gauss , Gosset , Hagen , Invariance , inverse probability , Laplace , least squares , likelihood limits , linear normal model , maximum likelihood , Merriman , method , posterior mode , reparameterization , t­distribution , two­stage maximum likelihood , unbiasedness

Rights: Copyright © 1999 Institute of Mathematical Statistics

Vol.14 • No. 2 • May 1999
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