Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables (Q898401)

Consider a sequence of random variables \(f(\xi_1),\dots,f(\xi_n)\), where \(\xi_1,\dots,\xi_n\) are independent and identically distributed, and \(f(\xi_1)\) has zero mean and finite second moment. This paper establishes a sharp bound for the tail probability of the supremum of the normalized sums of \(f(\xi_1),\dots,f(\xi_n)\) under various conditions, which are discussed in detail in the paper. The usefulness of these results in the study of the uniform central limit theorem is illustrated in the paper.