The oracle property of the generalized outcome adaptive lasso

TL;DR

This paper proves that the generalized outcome-adaptive lasso (GOAL) possesses the oracle property, ensuring optimal performance in high-dimensional causal inference, and demonstrates its advantages over the outcome-adaptive lasso (OAL) in simulations.

Contribution

It establishes the oracle property of GOAL, a variable selection method for high-dimensional causal inference, which was previously unproven.

Findings

GOAL enjoys the oracle property.

GOAL better handles collinearity than OAL.

Simulation results support GOAL's effectiveness.

Abstract

The generalized outcome-adaptive lasso (GOAL) is a variable selection for high-dimensional causal inference proposed by Bald\'e 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).