A Transferability Criterion for Null-Optimized Variance Reduction in Cumulant-Based Error-Independence Testing
基于累积量的误差独立性检验中零假设优化方差缩减的可迁移性准则
Control-variate and polynomial-maximization (PMM) estimators are optimized at a single fixed distribution, yet they are increasingly proposed to strengthen hypothesis tests, which decide between two regions of a parameter family. We give a closed-form criterion for when this transfer succeeds. For an H0-centered augmentation of a target moment statistic with null-optimized weight vector K0, the alternative-side expectation equals the target plus K0^T mu_a,H1, where mu_a,H1…