On the self-normalized Cramer-type large deviation

摘要

For the self-normalized sum, S-n/V-n, it is shown that P(S-n/V-n >= x)/(1-Phi(x)) converges to 1, uniformly in a region, under the optimal assumption that the sampled distribution is in the domain of attraction of the normal law. Bounds for this convergence are given and their applications to exponential non-uniform Berry-Esseen bound are also discussed.