Estimation

Estimation and inference for causal estimands: orthogonal moments and double machine learning, influence functions and asymptotic normality, efficiency bounds, cross-fitting, CATE learners, NPIV, and rate/coverage-facing results.

ATE 40 core · 41 supporting · 5 submodules Sample-split AIPW/DML estimation of the back-door average treatment effect: the moment function, its influence function, square-integrability, and the asymptotic-linearity theorem. Orthogonal­Moments 101 core · 54 supporting · 13 submodules Neyman-orthogonal moment functions: construction, cross-fitting, parametric examples, and automatic debiasing. Orthogonal­Learning 50 core · 11 supporting · 6 submodules Generic orthogonal statistical-learning substrate: population derivative bundles, cross-fitted plug-in ERM, local moduli, oracle inequalities, and sparse specializations. ATT 36 core · 35 supporting · 5 submodules Double machine learning for the average treatment effect on the treated (ATT) under back-door adjustment, using the score A·(Y − μ₀(X)) − (1 − A)·e(X)/(1 − e(X))·(Y − μ₀(X)) − A·θ, which involves only the control regress CATE 43 core · 13 supporting · 4 submodules Estimation of conditional average treatment effects: the DR-Learner, its oracle expansions, linear-smoother specializations, and orthogonal-statistical-learning analyses. DTR 49 core · 55 supporting · 11 submodules DML estimation for dynamic treatment regimes: the two-period AIPW moment, remainder identities and bounds, and the asymptotic-linearity theorem. Efficiency 80 core · 131 supporting · 14 submodules Semiparametric efficiency: tangent spaces, pathwise differentiability, and the efficiency bound for the ATE functional. Minimax­ATE 148 core · 174 supporting · 9 submodules This file is the entry point for the structure-agnostic lower- and upper-bound development for doubly robust average-treatment-effect estimation. NPIV 103 core · 68 supporting · 6 submodules Nonparametric instrumental variables: the conditional-moment operator, sieve primal analysis, ill-posedness measures, and doubly robust NPIV functionals. PLR 24 core · 22 supporting · 9 submodules Partially linear regression DML: Robinson partialling-out scores, nuisance bundles, mean-zero and remainder facts, Jacobian consistency, and one-step plus feasible asymptotic normality.