ABSTRACT

Motivated by the weak limit of Kolmogorov–Smirnov test statistics, in this contribution, we derive the asymptotics of $\mathbb{P}\left\{\underset{\mathit{x}\in [0,1{]}^n}{sup}\left(W\left(\mathit{x}\right)|W\left(\mathbf{1}\right)=w\right)>u\right\},w\in \mathbb{R},$for large u, where $W\left(\mathit{x}\right)$ is the multivariate Brownian sheet based on a distribution function F. The asymptotic results are obtained for general F and some important examples are also shown.

中文翻译：

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Kolmogorov-Smirnov 检验统计量的近似值

摘要

受 Kolmogorov-Smirnov 检验统计量的弱极限的启发，在这个贡献中，我们推导出渐近 $\mathbb{磷}\left\{\underset{\mathit{X}\in [0,1{]}^n}{超}\left(宽\left(\mathit{X}\right)|宽\left(\mathbf{1}\right)=瓦\right)>你\right\},瓦\in \mathbb{电阻},$对于大u，其中$宽\left(\mathit{X}\right)$是基于分布函数F的多元布朗表。得到了一般F的渐近结果，并给出了一些重要的例子。