Abstract
The strong consistency for maximum likelihood estimates is here studied following a method which differs consistently from the famous proof given by Wald [4] in 1949 and based on the likelihood ratio. Adopting an assumptions setting with a slight modification with respect to Wald, the proof is based on the interplay of two important tools: the first one is given by the uniformity of convergence via the Ranga Rao law of large numbers [3] for stochastic processes and the second one consists in a characterization of the identifiability conditions for the unknown parameter ϑ 0 stated by the author. The consistency result states that, with probability one, and when the number of observations is big enough, the likelihood function always admits at least one global maximizer and that, at the same time, all the possible global maximizers are strongly consistent estimates for the unknown parameter.
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