Abstract
Let X1, X2, … be i.i.d.r.v. and write (X1+…Xn−An)/Bn˜Fn, where Bn >0.AnER1, n≥1. It is known that solely one–sided asymptotic assumptions imposed on Fn imply Fn0. In the present note we show that stronger one–sided assumptions lead even to the existence of EX1 3 so that the BERRY-ESSEEN inequalities hold true.
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