Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples
Probabilistic Lower Bounds for the Discrepancy of Latin Hypercube Samples
复制标题
拉丁超立方样本差异的概率下界
DOI：
10.1007/978-3-319-72456-0_16
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发表时间：
2017
期刊：
影响因子：
--
通讯作者：
M. Gnewuch
中科院分区：
文献类型：
--
作者：
Benjamin Doerr;Carola Doerr;M. Gnewuch
我们提供了拉丁超立方体样本的星星差异的概率下界。这些界限是尖锐的意义上说，他们匹配最近的概率上界的星星差异的拉丁超立方体样本证明在Gnewuch和Hebbinghaus（离散界一类负相关随机点，包括拉丁超立方体样本。2016年预印本）。总之，这一结果和我们的工作意味着拉丁超立方体样本的差异最多从均匀采样点集的差异的常数因子不同。
We provide probabilistic lower bounds for the star discrepancy of Latin hypercube samples. These bounds are sharp in the sense that they match the recent probabilistic upper bounds for the star discrepancy of Latin hypercube samples proved in Gnewuch and Hebbinghaus (Discrepancy bounds for a class of negatively dependent random points including Latin hypercube samples. Preprint 2016). Together, this result and our work implies that the discrepancy of Latin hypercube samples differs at most by constant factors from the discrepancy of uniformly sampled point sets.