Orthogonal Inference for Conditional Z-Estimation without Cross-Fitting: A Distributional Nearest-Neighbor Approach

Abstract

Estimating conditional parameters, such as heterogeneous treatment effects, often requires rich covariate adjustment, even when the parameters are reported along only a few dimensions. Fitting nuisance functions on the full sample makes all observations available for adjustment, but creates dependence between fitted scores and the observations at which they are evaluated, which is typically avoided by cross-fitting. We develop pointwise inference with full-sample nuisance predictions for exactly identified conditional moment equations, recovering conditional average treatment effects as a special case. We localize the estimating equations around the reporting point using distributional nearest neighbors (DNN), a U-statistic-based averaging procedure. Under sufficient conditions on the local design, orthogonality, prediction accuracy and quantitative deletion stability, the estimator is asymptotically normal, and a frozen-score jackknife consistently estimates its limiting covariance with nuisance predictions held fixed. In simulations, full-sample and cross-fitted inference perform similarly, with coverage shortfalls from nuisance approximation error, spatial bias and heavy studentized tails. An application to 401(k) eligibility using Survey of Income and Program Participation data finds similar estimates across nuisance prediction methods, with wide normal-reference intervals.