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Media type:
E-Article
Title:
On the History of Maximum Likelihood in Relation to Inverse Probability and Least Squares
Contributor:
Hald, Anders
Published:
Institute of Mathematical Statistics, 1999
Published in:
Statistical Science, 14 (1999) 2, Seite 214-222
Language:
English
ISSN:
0883-4237
Origination:
Footnote:
Description:
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 [Grundzuge der Wahrschein-lichkeits-Rechnung, Dummler, 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 two-stage method of maximum likelihood he avoided appealing to unbiasedness for the linear normal model.