论文标题
通过Wasserstein和相关的积分概率指标界定Kolmogorov距离
Bounding Kolmogorov distances through Wasserstein and related integral probability metrics
论文作者
论文摘要
我们在两个概率分布之间的kolmogorov距离上建立了一般的上限，这些分布之间的距离与瓦斯坦斯坦或光滑的瓦斯汀指标相对于这些分布之间的距离。这些界限概括了文献中现有的结果。为了说明我们的一般边界的广泛适用性，我们将其应用于从Stein的方法文献中已建立的多元正常，beta和方差 - γ近似值中提取kolmogorov距离边界。
We establish general upper bounds on the Kolmogorov distance between two probability distributions in terms of the distance between these distributions as measured with respect to the Wasserstein or smooth Wasserstein metrics. These bounds generalise existing results from the literature. To illustrate the broad applicability of our general bounds, we apply them to extract Kolmogorov distance bounds from multivariate normal, beta and variance-gamma approximations that have been established in the Stein's method literature.
