On the consistency of the spacings test for multivariate uniformity, including on manifolds
On the consistency of the spacings test for multivariate uniformity, including on manifolds
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关于多元均匀性的间距测试的一致性，包括流形
DOI：
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发表时间：
2017
影响因子：
1
通讯作者：
N. Henze
中科院分区：
文献类型：
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作者：
N. Henze
本文给出了多元一致性检验在有界集K⊂ℝd上的一致性的一个简单的概念性证明，该检验是基于独立同分布的点X1，…生成的最大间隔。。.，Xn在K中，即包含在K中并避开这些点的给定形状的最大凸集的体积。由于d>；1情形的渐近结果只有在一致情况下才能得到，证明的一个关键因素是适当的耦合。这个证明足够普遍，足以涵盖由测地球定义的间距的紧致黎曼流形上的一致性测试的情况。
Abstract We give a simple conceptual proof of the consistency of a test for multivariate uniformity in a bounded set K ⊂ ℝd that is based on the maximal spacing generated by independent and identically distributed points X1, . . ., Xn 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 d > 1 case are only availabe under uniformity, a key element of the proof is a suitable coupling. The proof is general enough to cover the case of testing for uniformity on compact Riemannian manifolds with spacings defined by geodesic balls.