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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