Asymptotically Exact Constants in Natural Convergence Rate Estimates in the Lindeberg Theorem

Following (Shevtsova, 2013) we introduce detailed classification of the asymptotically exact constants in natural estimates rate convergence Lindeberg central limit theorem, namely Esseen’s, Rozovskii’s, and Wang–Ahmad’s inequalities their structural improvements obtained our previous works. The above involve algebraic truncated third-order moments classical fraction assume finiteness only second-order random summands. We present lower bounds for introduced as well universal most optimistic which turn to be not far from upper ones.