Article
On the Expected L2-Discrepancy of Stratified Samples from Parallel Lines
Authors
Abstract
We study the expected L 2-discrepancy of stratified samples gen- erated 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.
Keywords
Discrepancy, stratified sampling.
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
F. Pausinger, “On the expected L2-Discrepancy of stratified samples from parallel lines,” Uniform Distribution Theory, vol. 18, no. 2, pp. 31–56, 2023, doi: 10.2478/UDT-2023-0012.
Pausinger F. On the expected L2-Discrepancy of stratified samples from parallel lines. Uniform Distribution Theory. 2023;18(2):31–56. doi:10.2478/UDT-2023-0012.
Pausinger, F. (2023), ‘On the expected L2-Discrepancy of stratified samples from parallel lines’, Uniform Distribution Theory, 18(2), pp. 31–56. Available at: https://doi.org/10.2478/UDT-2023-0012.
Pausinger, Florian. “On the Expected L2-Discrepancy of Stratified Samples from Parallel Lines.” Uniform Distribution Theory, vol. 18, no. 2, 2023, pp. 31–56. https://doi.org/10.2478/UDT-2023-0012.
Pausinger, Florian. “On the Expected L2-Discrepancy of Stratified Samples from Parallel Lines.” Uniform Distribution Theory 18, no. 2 (2023): 31–56. https://doi.org/10.2478/UDT-2023-0012.
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Published by: Engineering Journals
