Permutation-Centered Henze–Zirkler Screening with Ties: Exact Finite-Sample Centering, Controlled Pairwise Approximation, and Field Assessment

PCHZ-SIS (permutation-centered tie-aware Henze–Zirkler sure independence screening) is a specialized marginal screening method for mixed data containing continuous and ordered–discrete predictors with extensive ties. The method combines tie-aware mid-rank Gaussianization, exact analytical computation of the conditional permutation means of the normalized Henze–Zirkler statistic, and a randomized incomplete-pair approximation. For the signed centered functional, an exact zero conditional expectation under the permutation null is established. For the incomplete-pair implementation, the uniform approximation error is of order log pM; for the oracle full-pair functional with fixed population transforms, the finite-sample bias of order 1n and stochastic error of order log pn are controlled separately. The empirical transform error is isolated as a separate term and bounded by a finite-sample DKW/Lipschitz argument; whether it vanishes asymptotically depends on the clipping regime. Preservation of the active set in the top-d ranking is guaranteed only under an explicit marginal separation condition, when the signal gap exceeds the combined statistical, transformation, and computational errors. In Monte Carlo experiments with n=200 and p=500, PCHZ-SIS achieved a mean TPR of 0.86 in the mixed/tied scenario versus 0 for HZ–common-clip, while DC-SIS remained the strongest general nonlinear comparator. Field assessment on 30 Tengiz wells showed that PCHZ-SIS reduced inflated HZ scores for several low-cardinality variables but did not improve downstream ridge performance relative to HZ–common-clip. PCHZ-SIS is therefore positioned as an HZ-specific finite-sample correction for severe ties rather than as a universal replacement for modern screening methods or a fully calibrated inferential testing procedure. A separate 200-replication confirmation experiment with n=200 and p=500 reproduced the severe ties finding using the exact published Xue–Liang truncation: PCHZ-SIS achieved a mean TPR of 0.885 versus 0 for HZ-Xue–Liang-clip; DC-SIS remained the strongest general nonlinear comparator (TPR 1.000), while SWD-SIS yielded TPR 0.425. A persistence-controlled Tengiz residual benchmark further evaluates the method; PCHZ-SIS improves over HZ-Xue–Liang-clip on this stricter endpoint without implying universal superiority over distance- or rank-based screens. An independent cross-domain field assessment on 180 complete haul-truck cycles further showed that PCHZ-SIS reduced downstream MAE from 1.598 ± 0.110 HEP percentage points for the two uncentered HZ clipping variants to 1.534 ± 0.088, while Spearman-SIS and DC-SIS remained slightly stronger (1.505 ± 0.104).