论文标题
新的分层随机抽样I：最佳预期星差异的星形差异
Star discrepancy for new stratified random sampling I: optimal expected star discrepancy
论文作者
论文摘要
我们介绍了一类凸的e象分区。在这些分区（包括简单的随机样品）下的分层样品中，比较了预期的星差结果。我们的结果有四个主要部分。首先，在这些新设计的分区中，有一个可以最大程度地减少预期的恒星差异，因此我们部分回答了[F. Pausinger，S。Steinerberger，J。Complex。 2016]。其次，有无限数量的这样的分区，它们的预期差异比大型抽样数字的经典抖动抽样较小，导致[M. Kiderlen，F。Pausinger，Monatsh。数学。 [2021]正在解决。第三，我们证明了一个强大的分区原则，并将这些分区模型下的预期星差异从$ l_2- $差异到星形差异，因此在[M. Kiderlen，F。Pausinger，J。Complex。 2021]回答。最后，给出了此类分区下的最佳预期星差上限，这比使用抖动的采样更好。
We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples. There are four main parts of our results. First, among these newly designed partitions, there is one that minimizes the expected star discrepancy, thus we partly answer an open question in [F. Pausinger, S. Steinerberger, J. Complex. 2016]. Second, there are an infinite number of such class of partitions, which generate point sets with smaller expected discrepancy than classical jittered sampling for large sampling number, leading to an open question in [M. Kiderlen, F. Pausinger, Monatsh. Math. 2021] being solved. Third, we prove a strong partition principle and generalize the expected star discrepancy under these partition models from $L_2-$discrepancy to star discrepancy, hence an open question in [M. Kiderlen, F. Pausinger, J. Complex. 2021] is answered. In the end, optimal expected star discrepancy upper bound under this class of partitions is given, which is better than using jittered sampling.
