Expected star discrepancy based on stratified sampling
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908752289988608 |
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| author | Xu, Xiaoda Xian, Jun |
| author_facet | Xu, Xiaoda Xian, Jun |
| contents | We present two main contributions to the expected star discrepancy theory. First, we derive a sharper expected upper bound for jittered sampling, improving the leading constants and logarithmic terms compared to the state-of-the-art [Doerr, 2022]. Second, we prove the strong partition principle for star discrepancy, showing that any equal-measure stratified sampling yields a strictly smaller expected discrepancy than simple random sampling, thereby resolving an open question in [Kiderlen and Pausinger, 2022]. Numerical simulations confirm our theoretical advances and illustrate the superiority of stratified sampling in low to moderate dimensions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_21504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Expected star discrepancy based on stratified sampling Xu, Xiaoda Xian, Jun Statistics Theory Probability We present two main contributions to the expected star discrepancy theory. First, we derive a sharper expected upper bound for jittered sampling, improving the leading constants and logarithmic terms compared to the state-of-the-art [Doerr, 2022]. Second, we prove the strong partition principle for star discrepancy, showing that any equal-measure stratified sampling yields a strictly smaller expected discrepancy than simple random sampling, thereby resolving an open question in [Kiderlen and Pausinger, 2022]. Numerical simulations confirm our theoretical advances and illustrate the superiority of stratified sampling in low to moderate dimensions. |
| title | Expected star discrepancy based on stratified sampling |
| topic | Statistics Theory Probability |
| url | https://arxiv.org/abs/2512.21504 |