Mallow距离中经验过程的收敛性及其在自举性能中的应用
Convergence of the empirical process in Mallows distance, with an application to bootstrap performance
摘要：
我们研究样本的经验分布和底层总体之间的Malows距离的收敛收敛速率。令人惊讶的特点，我们的结果是，收敛速度是在离散的情况下比在绝对连续的设置慢。我们展示了如何在这些计算中的危险函数起着重要的作用。作为一个应用程序，我们记得，研究的数量提供了一个样本均值的自助分布和它的真实抽样分布之间的距离的上界。此外，马洛斯度量的方便的性质产生一个简单的下界，因此在这个问题中的自助的渐近性能的相对精确的描述。
英文摘要：
We study the rate of convergence of the Mallows distance between the empirical distribution of a sample and the underlying population. The surprising feature of our results is that the convergence rate is slower in the discrete case than in the absolutely continuous setting. We show how the hazard function plays a significant role in these calculations. As an application, we recall that the quantity studied provides an upper bound on the distance between the bootstrap distribution of a sample mean and its true sampling distribution. Moreover, the convenient properties of the Mallows metric yield a straightforward lower bound, and therefore a relatively precise description of the asymptotic performance of the bootstrap in this problem.
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