On the Probability of Large Deviations of Families of Sample Means

Abstract

Results concerning the exponential convergence to zero of the probability of large deviations of the sample mean have already been obtained in the literature for instance, in Cramer [5], Chernoff [4], Bahadur and Rao [1], etc. We establish similar results about the exponential convergence to zero of the probability of large deviations of the sample distribution function, and more generally, of families of sample means.