论文标题
多个时间序列的最佳高斯近似
Optimal Gaussian Approximation for Multiple Time Series
论文作者
论文摘要
我们获得了最佳的结合，用于大型矢量值随机过程的高斯近似值。我们的结果提供了假定独立性和/或平稳性的早期结果的实质性概括。基于功能依赖度量的衰减率，我们使用样本大小$ n $和矩情况来量化高斯近似值的误差结合。在$ p $ th有限矩的假设下，$ p> 2 $，这可能从$ n^{1/2} $的最坏情况率到最佳案例率$ n^{1/p} $。
We obtain an optimal bound for a Gaussian approximation of a large class of vector-valued random processes. Our results provide a substantial generalization of earlier results that assume independence and/or stationarity. Based on the decay rate of the functional dependence measure, we quantify the error bound of the Gaussian approximation using the sample size $n$ and the moment condition. Under the assumption of $p$th finite moment, with $p>2$, this can range from a worst case rate of $n^{1/2}$ to the best case rate of $n^{1/p}$.
