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Journal

Uniform Distribution Theory (UDT)


Volume & Issue

UDT. Volume 18. Issue 2


Published on

December, 2023


Pages

31-56


DOI

https://doi.org/10.2478/udt-2023-0012

Article

On the Expected ℒ2-Discrepancy of Stratified Samples from Parallel Lines


Authors

Florian Pausinger


Abstract

We study the expected ℒ2-discrepancy of stratified samples generated from special equi-volume partitions of the unit square. The partitions are defined via parallel lines that are all orthogonal to the diagonal of the square. It is shown that the expected discrepancy of stratified samples derived from these partitions is a factor 2 smaller than the expected discrepancy of the same number of i.i.d uniformly distributed random points in the unit square. We conjecture that this is best possible among all partitions generated from parallel lines.


Citation

Pausinger, F. (2023). On the Expected ℒ2-Discrepancy of Stratified Samples from Parallel Lines. Uniform distribution theory, 18(2), 31-56. https://doi.org/10.2478/udt-2023-0012