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 39 core · 28 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 56 core · 8 supporting · 12 submodules Neyman-orthogonal moment functions: construction, cross-fitting, parametric examples, and automatic debiasing. Orthogonal­Learning 50 core · 7 supporting · 6 submodules Generic orthogonal statistical-learning substrate: population derivative bundles, cross-fitted plug-in ERM, local moduli, oracle inequalities, and sparse specializations. ATT 32 core · 30 supporting · 5 submodules AIPW/DML estimation of the average treatment effect on the treated (Hahn-form moment), mirroring the ATE development; the top-level theorem files are pending repair against the current Mathlib pin. 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 47 core · 49 supporting · 11 submodules DML estimation for dynamic treatment regimes: the two-period AIPW moment, remainder identities and bounds, and the asymptotic-linearity theorem. Efficiency 25 core · 35 supporting · 6 submodules Semiparametric efficiency: tangent spaces, pathwise differentiability, and the efficiency bound for the ATE functional. Gauss­Markov 12 core · 8 supporting · 5 submodules The Gauss-Markov theorem for linear models: best linear unbiased estimation under spherical errors. Minimax­ATE 143 core · 171 supporting · 9 submodules This file is the entry point for the structure-agnostic optimality development for doubly robust average-treatment-effect estimation. NPIV 89 core · 53 supporting · 6 submodules Nonparametric instrumental variables: the conditional-moment operator, sieve primal analysis, ill-posedness measures, and doubly robust NPIV functionals. PLR 25 core · 18 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.