Esseen–Rozovskii Type Estimates for the Rate of Convergence in the Lindeberg Theorem
Esseen–Rozovskii Type Estimates for the Rate of Convergence in the Lindeberg Theorem
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Lindeberg 定理收敛率的 Esseen-Rozovskii 型估计
DOI：
10.1007/s10958-018-4051-2
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发表时间：
2018
影响因子：
--
通讯作者：
I. Shevtsova
中科院分区：
文献类型：
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作者：
R. Gabdullin;V. Makarenko;I. Shevtsova
我们提出了 Esseen（1969）和 Rozovskii（1974）对 Lindeberg 定理收敛率估计的结构改进，并计算了出现的绝对常数。我们在构造的不等式中引入渐近精确常数并获得它们的上限。我们分析了 Esseen、Rozovskii 和 Lyapunov 分数的值，将它们成对比较，并提供一些极值分布。作为辅助陈述，我们证明了任意分布（具有有限二阶矩）的二次尾部的锐不等式及其卷积对称性。
We present structural improvements of Esseen’s (1969) and Rozovskii’s (1974) estimates for the rate of convergence in the Lindeberg theorem and also compute the appearing absolute constants. We introduce the asymptotically exact constants in the constructed inequalities and obtain upper bounds for them. We analyze the values of Esseen’s, Rozovskii’s, and Lyapunov’s fractions, compare them pairwise, and provide some extremal distributions. As an auxiliary statement, we prove a sharp inequality for the quadratic tails of an arbitrary distribution (with finite second-order moment) and its convolutional symmetrization.