关于多元均匀性间隔检验的一致性
On the consistency of the spacings test for multivariate uniformity
摘要：
我们给出了一个简单的概念性证明的一致性测试多元均匀性的有界集$K \subset \mathbb{R}^d$是基于由i.i.d.产生的最大间距。在$K$中的点$X_1, \ldots,X_n$，即，包含在$K$中且避开这些点的给定形状的最大凸集的体积。由于$d > 1$情形的渐近结果仅在一致性条件下有效，证明的关键要素是适当的耦合。
英文摘要：
We give a simple conceptual proof of the consistency of a test for multivariate uniformity in a bounded set $K \subset \mathbb{R}^d$ that is based on the maximal spacing generated by i.i.d. points $X_1, \ldots,X_n$ in $K$, i.e., the volume of the largest convex set of a given shape that is contained in $K$ and avoids each of these points. Since asymptotic results for the case $d > 1$ are only availabe under uniformity, a key element of the proof is a suitable coupling.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
