The oracle property of the generalized outcome adaptive lasso

The generalized outcome-adaptive lasso (GOAL) is a variable selection for high-dimensional causal inference proposed by Baldé et al. [2023, {\em Biometrics} {\bfseries 79(1)}, 514–520]. When the dimension is high, it is now well established that an ideal variable selection method should have the oracle property to ensure the optimal large sample performance. However, the oracle property of GOAL has not been proven. In this paper, we show that the GOAL estimator enjoys the oracle property. Our simulation shows that the GOAL method deals with the collinearity problem better than the oracle-like method, the outcome-adaptive lasso (OAL).