Optimal Neyman-orthogonal Subsampling for Partially Linear Mediation Models

In this paper, we propose three effect-specific optimal subsampling strategies for estimating direct, total and indirect effects in partially linear mediation models with high-dimensional confounders. We construct two inverse-probability weighted subsampling Neyman-orthogonal score functions for the direct and total effects, respectively, to simultaneously eliminate selection bias and regularization bias. The unconditional asymptotic distributions of three subsample effect estimators are established and then we derive effect-specific optimal subsampling probabilities by minimizing the traces of their asymptotic variances. A two-step procedure is proposed for practical implementation by using flexible machine learning and data splitting techniques to estimate the high-dimensional nuisance functions and address potential overfitting. Extensive simulations demonstrate the superior performance of the proposed subsample estimators and an application to a real-world air pollution dataset further confirms the practical utility.