Kybernetika 31 no. 1, 45-64, 1995

On consistency of the MLE

František Rublík


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, 62F10, 62B99