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The Partition Principle Revisited: Non-Equal Volume Designs Achieve Minimal Expected Star Discrepancy
Xiaoda Xu
We study the expected star discrepancy under a newly designed class of non-equal volume partitions. The main contributions are twofold. First, we establish a strong partition princ…
On a Class of Partitions with Lower Expected Star Discrepancy and Its Upper Bound than Jittered Sampling
Xiaoda Xu, Jun Xian
We investigate the expected star discrepancy under a newly designed class of convex equivolume partition models. The main contributions are two-fold. First, we establish a strong p…
Sharp Non-Asymptotic Bounds for the Star Discrepancy of Double-Infinite Random Matrices via Optimal Covering Numbers
Xiaoda Xu, Jun Xian
We establish sharp non-asymptotic probabilistic bounds for the star discrepancy of double-infinite random matrices -- a canonical model for sequences of random point sets in high d…
Expected star discrepancy based on stratified sampling
Xiaoda Xu, Jun Xian
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 an…