Research

When evaluating the impacts of policies, average treatment effects can conceal differences across units that matter for policy design and implementation. Estimating these differences often requires rich covariate adjustment, even when effects are reported along only a few dimensions. Yet even with large training samples, localization can leave little effective information at a given covariate profile. This creates a tension between learning nuisance functions from the full sample and controlling their influence on an estimator whose uncertainty is determined locally. We develop pointwise inference for exactly identified conditional moment equations that are affine in a fixed-dimensional target, allowing observation-varying, nuisance-dependent coefficients and recovering conditional average treatment effects as a special case. We localize the estimating equations relative to the target using distributional nearest neighbors (DNN), a U-statistic-based averaging procedure. Under suitable undersmoothing, oracle and learner conditions, and quantitative deletion stability, we establish valid inference using full-sample nuisance fits without cross-fitting and exploiting orthogonality. The resulting estimator is asymptotically normal, and a frozen-score jackknife consistently estimates its limiting covariance without requiring leave-one-out nuisance refits. The exact DNN rank weights allow all jackknife deletions to be computed in linear time after sorting distances. Simulations show that agreement between full-sample and cross-fitted estimates can coexist with approximation error, spatial bias and studentization problems that reduce point coverage. An application to the Survey of Income and Program Participation 401(k) data finds similar but imprecise eligibility estimates across nuisance-training schemes, alongside limited local information, uneven treatment support and concentrated fitted uncertainty.

Many subsampling-based and randomized estimators admit generalized U-statistic representations, but their variance-estimation theory remains less developed than their pointwise asymptotics. We prove ratio consistency of ordinary and delete-d jackknife variance estimators under a variance-ratio condition ensuring Hájek-projection dominance and a row-wise weak law for normalized squared first projections. Classical U-statistics with fixed order s ≥ 2 are included as a special case. For Bernoulli-incomplete generalized U-statistics, the same ratio-consistency conclusion holds under an additional asymptotically sufficient sampling condition. This makes Bernoulli-sampling noise and realized-count normalization error negligible on the first-projection scale. Our application to two-scale distributional nearest-neighbor regression weakens the kernel-order requirement for jackknife variance consistency from s₂ = o(n^1/3) to s₂ = o(n) for fixed d.