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On the Expected L2−discrepancy of Jittered Sampling
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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.
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Published by: Engineering Journals


