Expected L_2-discrepancy bound for a class of new stratified sampling models

04/19/2022

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by   Jun Xian, et al.

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We introduce a class of convex equivolume partitions. Expected L_2-discrepancy are discussed under these partitions. There are two main results. First, under this kind of partitions, we generate random point sets with smaller expected L_2-discrepancy than classical jittered sampling for the same sampling number. Second, an explicit expected L_2-discrepancy upper bound under this kind of partitions is also given. Further, among these new partitions, there is optimal expected L_2-discrepancy upper bound.