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On the History of Maximum Likelihood in Relation to Inverse Probability and Least Squares

Anders Hald
Statistical Science
Vol. 14, No. 2 (May, 1999), pp. 214-222
Stable URL: http://www.jstor.org/stable/2676741
Page Count: 9
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On the History of Maximum Likelihood in Relation to Inverse Probability and Least Squares
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Abstract

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.

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