Valid uncertainty quantification for subsampling-based and randomized estimators often depends on variance estimators whose behavior is much less understood than that of the underlying point estimator. We prove ratio-consistency of the jackknife variance estimator, and certain delete-$d$ variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their Hajek projection and whose normalized first-projection squares satisfy a row-wise $L^r$ weak law, with the classical fixed-order case recovered as a special instance. This projection-dominance plus square-LLN structure unifies and generalizes several criteria from the existing literature, clarifies when the simple nonparametric jackknife is theoretically justified in the generalized setting, and yields consistent variance estimation for the two-scale distributional nearest-neighbor regression estimator under substantially weaker conditions than previously required.

翻译：摘要：基于子抽样和随机化估计量的有效不确定性量化通常依赖于方差估计量，而其行为远不如底层点估计量为人所理解。我们证明了对一类广义U统计量的Jackknife方差估计量及其某些删除-d变体的比率一致性。这类统计量的方差渐近地由其Hájek投影主导，且其归一化一阶投影平方满足行向L^r弱大数定律，经典固定阶情形作为特例被包含在内。这种投影主导加平方大数定律结构统一并推广了现有文献中的若干准则，阐明了简单非参数Jackknife在广义设定下何时具有理论依据，并在比先前所需条件显著更弱的假设下，为两尺度分布最近邻回归估计量导出了相合方差估计。