Sharp tail distribution estimates for the supremum of a class of sums of i.i.d. random variables
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.
scientific article; zbMATH DE number 6518038