An optimal Berry-Esseen type inequality for expectations of smooth functions


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Аннотация

We provide an optimal Berry-Esseen type inequality for Zolotarev’s ideal ζ3-metric measuring the difference between expectations of sufficiently smooth functions, like |·|3, of a sum of independent random variables X1,..., Xn with finite third-order moments and a sum of independent symmetric two-point random variables, isoscedastic to the Xi. In the homoscedastic case of equal variances, and in particular, in case of identically distributed X1,..., Xn the approximating law is a standardized symmetric binomial one. As a corollary, we improve an already optimal estimate of the accuracy of the normal approximation due to Tyurin (2009).

Авторлар туралы

L. Mattner

FB IV – Mathematics

Email: ishevtsova@cs.msu.ru
Германия, Trier

I. Shevtsova

Hangzhou Dianzi University; Faculty of Computational Mathematics and Cybernetics of Lomonosov Moscow State University; Institute for Informatics Problems of FRC IC RAS

Хат алмасуға жауапты Автор.
Email: ishevtsova@cs.msu.ru
ҚХР, Hangzhou; Moscow; Moscow

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