Estimation.CATE.OrthogonalLearning
DR-Learner orthogonal-learning system and oracle inequalities for CATE, including analytic derivatives, empirical-process moduli, and random-nuisance variants.
SecondOrderBias 1 core · 0 supporting This file shows that the nuisance-induced bias in the doubly robust learner for conditional treatment effects is bounded by the product of the outcome-regression error and the propensity-score error. ★ drBias_le_product
DR-Learner Second-Order Bias
This file shows that the nuisance-induced bias in the doubly robust learner for conditional treatment effects is bounded by the product of the outcome-regression error and the propensity-score error. The result makes the double-robust second-order remainder in the orthogonal statistical-learning oracle inequality explicit.
DR-Learner second-order product bias bound. For a CATE estimation system built on a potential-outcome model that satisfies the back-door identification assumptions, with the true nuisance η₀ lying in the strict-overlap band at some margin ε > 0, fix a convex candidate target class in an inner-product space with a real-valued evaluation map, and suppose θ₀ belongs to this class, every candidate's evaluation is measurable, θ₀'s evaluation agrees pointwise with the true value-space CATE, and θ₀ minimizes the true-nuisance population squared pseudo-outcome risk over the class. Fix evaluation and nuisance directional-derivative bundles and a candidate nuisance h that also lies in the strict-overlap band at the same margin, a candidate target θ̂, and a nonnegative constant B bounding the evaluation-map directional derivative at θ̂. Assume the arm-wise outcome-regression fit of h, the AIPW pseudo-outcome discrepancy between h and the truth, and that discrepancy weighted by the directional derivative are all integrable, the outcome-regression error of h and the propensity error of h are square-integrable arm by arm, and the loss-gradient integrand at the true nuisance and the loss-gradient integrand at the candidate nuisance h are each integrable against the observation law. Then the loss-gradient nuisance bias Bias_n, evaluated between the true and candidate nuisance directional derivatives at θ̂, is bounded in absolute value by (2B/ε) times the sum over treatment arms of the outcome-regression L² error times the propensity L² error.