Expected L₂-discrepancy bound for a class of new stratified sampling models

2022/04/19 by Jun Xian, Xian, Jun, Xiaoda Xu +1
Mathematics · #Mathematical Approximation and Integration #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.2204.08752

Abstract

We introduce a class of convex equivolume partitions. Expected L₂-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 L₂-discrepancy than classical jittered sampling for the same sampling number. Second, an explicit expected L₂-discrepancy upper bound under this kind of partitions is also given. Further, among these new partitions, there is optimal expected L₂-discrepancy upper bound.

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