2025/12/25 by Xiaoda Xu, Xu, Xiaoda, Jun Xian +1
Mathematics · #Benford’s Law and Fraud Detection #FOS: Mathematics #Markov Chains and Monte Carlo Methods #Mathematical Approximation and Integration #Probability (math.PR) #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.2512.21504
openalex publication_date 2025/12/25 · openalex created_date 2025/12/30 · openalex updated_date 2026/07/28
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.