Some optimal bounds in the central limit theorem using zero biasing
A wide class of probability metrics is concerned. Optimal estimates for the proximity between a probability distribution and its zero bias transformation are derived. The reduction technique of Hoeffding is used. A theorem concerning the bounds of convergence in the central limit theorem is formulated and proved when the moments of order \(2< s\leq 3\) are finite, using the ideal metrics introduced by Zolotarev.
scientific article; zbMATH DE number 6036272