Explain the SRP+KS deviation at large sample size

Explain quantitatively why the SRP+KS detection accuracy at sample sizes of 1,000 and 10,000 deviates from the published Failing Loudly results, particularly the deviation at N = 1,000.

Background

The paper reproduces the Failing Loudly benchmark and reports generally small mean absolute errors across the evaluated tests. However, the largest individual deviations occur for SRP+KS at N = 10 and N = 1,000. The N = 10 discrepancy is attributed to the discreteness of the Bonferroni-corrected KS null distribution, but the authors do not provide a complete quantitative explanation for the N = 1,000 discrepancy.

References

The largest single-cell deviations are for SRP+KS at N = 10 (-0.140) and at N = 1000 (-0.137); the former is consistent with the discreteness of the KS null distribution at N = 10 under Bonferroni over 32 projected dimensions, and the latter has been examined in supplementary analysis but a fully quantitative explanation remains open.

— Beyond Marginal Monitoring: Distributed Joint-Distribution Testing for Data Concept Drift in Large Scale E-Commerce Operations  (2610.08132 - Pullu et al., 6 Oct 2026) in Section 6.2.1, Reproduction accuracy