Large Deviation Theorems for Empirical Probability Measures
Open Access
- 1 August 1979
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Probability
- Vol. 7 (4) , 553-586
- https://doi.org/10.1214/aop/1176994984
Abstract
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.Keywords
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