BERRY-ESSEEN THEOREMS UNDER WEAK DEPENDENCE
BERRY-ESSEEN THEOREMS UNDER WEAK DEPENDENCE
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DOI：
10.1214/15-aop1017
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发表时间：
2016-05-01
影响因子：
2.3
通讯作者：
Jirak, Moritz
中科院分区：
文献类型：
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作者：
Jirak, Moritz
令 {X-k}(k >= Z) 为平稳序列。给定 p 是 (2, 3] 矩的元素和轻微的弱相关条件，我们展示了最优速率 n(p/2-1) 的 Berry-Esseen 定理。对于 p >= 4，我们还展示了 L-q-范数中 n(1/2) 的收敛速率，其中 q >= 1。直到 log n 因子，我们还获得了任何 p > 2 的非均匀速率。这为时间序列中的许多线性和非线性过程带来了新的最优结果文献，还包括动力系统理论的例子，证明基于特征函数、耦合和条件参数以及理想度量的混合方法。
Let {X-k}(k >= Z) be a stationary sequence. Given p is an element of (2, 3] moments and a mild weak dependence condition, we show a Berry-Esseen theorem with optimal rate n(p/2-1). For p >= 4, we also show a convergence rate of n(1/2) in L-q-norm, where q >= 1. Up to log n factors, we also obtain nonuniform rates for any p > 2. This leads to new optimal results for many linear and nonlinear processes from the time series literature, but also includes examples from dynamical system theory. The proofs are based on a hybrid method of characteristic functions, coupling and conditioning arguments and ideal metrics.