Uniform Distribution Theory
Journal license

Journal

Uniform Distribution Theory


Volume
& Issue

Volume 18, Issue 1


Published
on

February 27, 2023


Pages

65-82


DOI

Article

On the Expected L2−discrepancy of Jittered Sampling

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Authors

Nathan Kirk Affiliation:
Florian Pausinger School of Mathematics and Physics Queen’s University Belfast University Road BT7 1NN UNITED KINGDOM
and Florian Pausinger Affiliation:
School of Mathematics and Physics Queen’s University Belfast University Road BT7 1NN, Belfast UNITED KINGDOM


Abstract

For m, d ∈ N, a jittered sample of N = md points can be con- structed by partitioning [0, 1]d into md axis-aligned equivolume boxes and plac- ing one point independently and uniformly at random inside each box. We utilise a formula for the expected L 2 −discrepancy of stratified samples stemming from general equivolume partitions of [0, 1]d which recently appeared, to derive a closed form expression for the expected L 2 −discrepancy of a jittered point set for any m, d ∈ N. As a second main result we derive a similar formula for the expected Hickernell L 2 −discrepancy of a jittered point set which also takes all projections of the point set to lower dimensional faces of the unit cube into account.


Keywords

jittered sampling, star-discrepancy, L 2-discrepancy, Hickernell L 2-discrepancy.


Citation

Kirk, N. & Pausinger, F. (2023). On the expected L2−discrepancy of jittered sampling. Uniform Distribution Theory, 18(1), 65–82. https://doi.org/10.2478/UDT-2023-0005

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