The maximum likelihood estimator only exists for samples for which the sample variance is larger than the sample mean.
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For many models, a maximum likelihood estimator can be found as an explicit function of the observed data.
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Maximum spacing estimators are also at least as asymptotically efficient as maximum likelihood estimators, where the latter exist.
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Thus the Bayesian estimator coincides with the maximum likelihood estimator for a uniform prior distribution P ( \ theta ).
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Takeshi Amemiya ( 1973 ) has proven that the maximum likelihood estimator suggested by Tobin for this model is consistent.
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I've also read on the internet the maximum likelihood estimator might be better than linear regression for power laws.
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Following the parametrized probability mass function used to calculate the maximum likelihood estimator, is important to corroborate the following hypothesis,
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Two-step M-estimator involving Maximum Likelihood Estimator is a special case of general two-step M-estimator.
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However, as was shown by, the maximum likelihood estimator is "'not "'third-order efficient.
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An alternative derivation of the maximum likelihood estimator can be performed via matrix calculus formulae ( see also differential of the inverse matrix ).
