The Berry-Esseen bound for self-normalized sums
First, the author estimates a constant in the Berry-Esseen bound for self-normalized sums of independent identically distributed random variables. He obtains different versions of the Berry-Esseen bound, namely, under the assumption of the third or sixth moments and for bounded random variables. His approach to prove the Berry-Esseen bound differs principally from that accepted by V. Bentkus and F. Götze. In the case when sixth moment is finite, the author compares his result with that which can be derived from bounds on the remainder in the two-dimensional central limit theorem.
scientific article; zbMATH DE number 2097081