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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…
Star discrepancy bounds based on Hilbert space filling curve stratified sampling and its applications
Jun Xian, Xiaoda Xu
In this paper, we consider the upper bound of the probabilistic star discrepancy based on Hilbert space filling curve sampling. This problem originates from the multivariate integr…
Expected discrepancy bound for a class of new stratified sampling models
Jun Xian, Xiaoda Xu
We introduce a class of convex equivolume partitions. Expected discrepancy are discussed under these partitions. There are two main results. First, under this kind of partiti…
Star discrepancy for new stratified random sampling I: optimal expected star discrepancy
Jun Xian, Xiaoda Xu, Xinkai Zhou
We introduce a class of convex equivolume partitions. Expected star discrepancy results are compared for stratified samples under these partitions, including simple random samples.…