Some theorems on first-order asymptotic behavior of probabilities of large deviations of empirical probability measures are proved. These theorems extend previous results due to Borovkov, Hoadley and Stone. A multivariate analogue of Chernoff's theorem and a large deviation result for trimmed means are obtained as particular applications of the general theory.
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Groeneboom et al. (1979) studied this question.
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