On consistency of the MLE. (English) Zbl 0858.62022

Summary: Convergence of the maximum likelihood estimator is established without the assumption that the true value of the parameter belongs to the null hypothesis \(\Omega_0\). It is shown, that the MLE exists with probability tending to 1, and that the distance of the MLE from a set \(H\) of parameters from \(\Omega_0\) tends to zero almost everywhere, where \(H\) are parameters of the probabilities best fitting the true distribution in the sense that they maximize the mean of logarithm of the likelihood function.


62F12 Asymptotic properties of parametric estimators
62B99 Sufficiency and information
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