An optimal Berry-Esseen type inequality for expectations of smooth functions
| Autor: | Lutz Mattner, Irina Shevtsova |
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| Rok vydání: | 2017 |
| Předmět: |
Discrete mathematics
Independent and identically distributed random variables Ideal (set theory) Binomial (polynomial) General Mathematics 010102 general mathematics Type inequality 01 natural sciences 010104 statistics & probability Corollary Homoscedasticity Normal approximation Applied mathematics 0101 mathematics Random variable Mathematics |
| Zdroj: | Doklady Mathematics. 95:250-253 |
| ISSN: | 1531-8362 1064-5624 |
| Popis: | 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 X 1,..., X n with finite third-order moments and a sum of independent symmetric two-point random variables, isoscedastic to the X i . In the homoscedastic case of equal variances, and in particular, in case of identically distributed X 1,..., X n 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). |
| Databáze: | OpenAIRE |
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