Adaptive-to-sub-null testing for mediation effects in structural equation models

To effectively implement large-scale hypothesis testing of causal mediation effects and control false discovery rate (FDR) for linear structural equation models, this paper proposes an Adaptive-to-Sub-Null test (AtST) tailored specifically for the assessment of multidimensional mediation effects. The significant distinction of AtST from existing methods is that for every mediator, the weak limits of the test statistic under all mutually exclusive sub-null hypotheses uniformly conform to a chi-square distribution with one degree of freedom. Therefore, in the asymptotic sense, the significance level can be maintained and the p-values can be computed easily without any other prior information on the sub-null hypotheses or resampling technique. In theoretical investigations, we extend existing parameter estimation methods by allowing lower sparsity level in high-dimensional covariate vectors. These results offer a solid base for better FDR control by directly applying the classical Storey's method. We also apply a data-driven approach for selecting the tuning parameter of Storey's estimator. Simulations are conducted to demonstrate the efficacy and validity of the AtST, complemented by an analytical exploration of a genuine dataset for illustration.