{"ID":2825127,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.21504","arxiv_id":"2512.21504","title":"Expected star discrepancy based on stratified sampling","abstract":"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.","short_abstract":"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, sh...","url_abs":"https://arxiv.org/abs/2512.21504","url_pdf":"https://arxiv.org/pdf/2512.21504v2","authors":"[\"Xiaoda Xu\",\"Jun Xian\"]","published":"2025-12-25T04:25:46Z","proceeding":"math.ST","tasks":"[\"math.ST\",\"math.PR\"]","methods":"[]","has_code":false}