Generalised regression estimators for average treatment effect with multicollinearity in high-dimensional covariates

Abstract

In the simulation 1, the observed sample sizes under treated and control are almost equal, i.e., E(T ) is about 0.5. The variable selection results are given in Table S1. To investigate the effect of different sample sizes under treatment and control groups, we consider the following two cases:Using the same α = (0.6, 0.6, 0.6, 0, • • • , 0) T , we have E(T ) ≈ 0.38 and 0.64, respectively. The simulation results are shown in Figures S1-S2 and Table S2. We have the similar conclusions as in the simulation 1. No matter the observed sample sizes under the treated group are large or small, the proposed estimator θEnet GREG still performs well in terms of bias, SD and MSE. In addition, the regularized method based on the Elastic-net can select covariates more correctly, i.e., it has larger correct rates and smaller incorrect rates compared with the Lasso method.