Improved expected $L_2$-discrepancy formulas on jittered sampling

TL;DR

This paper derives improved formulas for the expected $L_2$-discrepancy in jittered sampling, providing more accurate assessments of sampling uniformity.

Contribution

It introduces new explicit and exact formulas for expected $L_2$-discrepancy, surpassing previous jittered sampling estimates.

Findings

Derived explicit formulas for expected $L_2$-discrepancy.

Derived exact formulas for expected $L_2$-discrepancy.

Results show improved discrepancy estimates over traditional jittered sampling.

Abstract

We study the expected $ L_2-$discrepancy under two classes of partitions, explicit and exact formulas are derived respectively. These results attain better expected $L_2-$discrepancy formulas than jittered sampling.