On a partition with a lower expected $\mathcal{L}_2$-discrepancy than classical jittered sampling

Markus Kiderlen; Florian Pausinger

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arXiv · 2106.01937

On a partition with a lower expected $\mathcal{L}_2$-discrepancy than classical jittered sampling

Markus Kiderlen·Florian Pausinger

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Abstract

We prove that classical jittered sampling of the $d$-dimensional unit cube does not yield the smallest expected $\mathcal{L}_2$-discrepancy among all stratified samples with $N=m^d$ points. Our counterexample can be given explicitly and consists of convex partitioning sets of equal volume.

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Markus Kiderlen, Florian Pausinger. 2021-06-03. On a partition with a lower expected $\mathcal{L}_2$-discrepancy than classical jittered sampling. https://arxiv.org/abs/2106.01937

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