Asymptotic upper and lower bounds are obtained for the uniform measure of the rate of convergence in the central limit theorem using a variety of norming constants. For many distributions the upper and lower bounds are of the same order of magnitude. As easy corollaries we deduce extensive generalizations of the classical characterizations of the rate of convergence in terms of series and order of magnitude conditions.
"Characterizing the Rate of Convergence in the Central Limit Theorem." Ann. Probab. 8 (6) 1037 - 1048, December, 1980. https://doi.org/10.1214/aop/1176994566