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arXiv · 2204.08752

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

Jun Xian·Xiaoda Xu
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Abstract

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.

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Jun Xian, Xiaoda Xu. 2022-04-19. Expected $L_2-$discrepancy bound for a class of new stratified sampling models. https://arxiv.org/abs/2204.08752

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