Higher-Order Influence Function Estimators for the Average Treatment Effect

Implements Higher-Order Influence Function (HOIF) estimators of the Average Treatment Effect (ATE), following Robins et al. (2008) , Liu et al. (2017) and Liu and Li (2023) . Estimators of any order are supported, with optional covariate basis transformations (B-splines, Fourier) and optional K-fold sample splitting (cross-fitting) for improved finite-sample performance. The core higher-order U-statistics are computed exactly via the 'ustats' package, an R interface to the 'Python' package 'u-stats'; the underlying algorithm and its computational complexity are analyzed in Chen, Zhang and Liu (2025) . A pure R implementation (up to order 6) is also provided as a fallback that does not require 'Python'.