The Doubly Robust or the Augmented Inverse Propensity Score Weighting Estimator for the Average Causal Effect
Peng Ding · 2024
Under ignorability https://www.w3.org/1998/Math/MathML" display="inline"> Z ⊥ ⊥ { Y ( 1 ) , Y ( 0 ) } ∣ X https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003484080/65a161dd-5ee1-4621-8dac-3405085a7197/content/math12_1.tif "/> and overlap https://www.w3.org/1998/Math/MathML" display="inline"> 0 , Chapter 11 has shown two identification formulas of the average causal effect https://www.w3.org/1998/Math/MathML" display="inline"> τ = E { Y ( 1 ) − Y ( 0 ) } https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003484080/65a161dd-5ee1-4621-8dac-3405085a7197/content/math12_3.tif "/> . First, the outcome regression formula is 12.1 https://www.w3.org/1998/Math/MathML" display="block"> τ = E { μ 1 ( X ) } − E { μ 0 ( X ) } https://www.w3.org/1999/xlink" xlink:href=" https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9781003484080/65a161dd-5ee1-4621-8dac-3405085a7197/content/math12_4.tif "/>