Probabilities of moderate deviations under m‐dependence

Abstract

AbstractConsider a stationary sequence {X1, X2,… } of m‐dependent random variables. It is proved that for any constant c > 0, if E|X1|p < ∞ for some p > c2 + 2, then and as n → ∞, where μ = E(X1) and The above results on probabilities of moderate deviations for sample means are then used to obtain similar results for U‐statistics and Von Mises' differentiable statistical functions when the underlying variables form a stationary m‐dependent sequence.