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.
Publié le : 1999-05-14
Classification:
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,
posterior mode,
reparameterization,
tdistribution,
twostage maximum likelihood,
method,
unbiasedness
@article{1009212248,
author = {Hald, Anders},
title = {On the history of maximum likelihood in relation to inverse
probability and least squares},
journal = {Statist. Sci.},
volume = {14},
number = {1},
year = {1999},
pages = { 214-222},
language = {en},
url = {http://dml.mathdoc.fr/item/1009212248}
}
Hald, Anders. On the history of maximum likelihood in relation to inverse
probability and least squares. Statist. Sci., Tome 14 (1999) no. 1, pp. 214-222. http://gdmltest.u-ga.fr/item/1009212248/