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Epi-convergence of sequences of normal integrands and strong consistency of the maximum likelihood estimator. (English) Zbl 0862.62029
Summary: Using the variational properties of epi-convergence together with suitable results on the measurability of multifunctions and integrands, we prove a strong law of large numbers for sequences of integrands form which we deduce a general theorem of almost sure convergence (strong consistency) for the maximum likelihood estimator.

62F12 Asymptotic properties of parametric estimators
60F15 Strong limit theorems
28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections
49K45 Optimality conditions for problems involving randomness
Full Text: DOI
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