Research

We prove ratio-consistency of the jackknife variance estimator, and certain variants, for a broad class of generalized U-statistics whose variance is asymptotically dominated by their Hájek projection, with the classical fixed-order case recovered as a special instance. This Hájek projection dominance condition unifies and generalizes several criteria in the existing literature, placing the simple nonparametric jackknife on the same footing as the infinitesimal jackknife in the generalized setting. As an illustration, we apply our result to the two-scale distributional nearest-neighbor regression estimator, obtaining consistent variance estimates under substantially weaker conditions than previously required.

We develop pointwise inference for parameters defined by localized conditional estimating equations, such as conditional average treatment effects and quantile-regression slopes at a fixed covariate profile. The estimator uses distributional nearest-neighbor weights with orthogonal scores and a leave-one-out stability condition, allowing same-sample machine-learned nuisance estimates without cross-fitting in sparse local neighborhoods. The theory gives asymptotic normality and feasible inference through a jackknife variance estimator and localized finite-difference Jacobian.