Results on Probabilities of Moderate Deviations

Abstract

The convergence rate problem for probabilities of moderate deviations is completely solved by giving a necessary and sufficient condition for the existence of the absolute moment of order $c^2 + 2, c > 0$, in terms of probabilities of moderate deviations. Furthermore, a result on the rate of convergence of probabilities of moderate deviations is given under a weaker moment condition than in Rubin and Sethuraman (1965).