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.