Abstract

Detecting the absence of the mediation effect is a major focus of mediation analysis. When treatment does not influence mediators that do not affect the outcome, testing the natural indirect effect is an interesting issue in the recent literature, since the asymptotic distributions of existing test statistics vary under different sub-null hypotheses. This paper introduces a novel statistical inference procedure tailored for high-dimensional mediation structures to address the issue of test conservativeness under some nontrivial sub-null hypotheses. We first suggest an estimation procedure using a partial penalized least squares estimation and compute the inner product of the treatment-mediator coefficient and the mediator-outcome coefficient. Based on the product, we develop a Wald-type test to handle the case where the mediator affects the outcome. As when the mediators do not affect the outcome, the Wald-type test statistic fails to maintain the significance level, we then construct another test for the significance level maintenance. The final test is an adaptive-to-sub-null hybrid of the two tests, which can flexibly accommodate different sub-null hypotheses and ensures that the limiting null distribution converges to a Chi-Square distribution uniformly across all sub-null hypotheses. Numerical simulations are conducted to assess the finite sample performances of the proposed test and make comparisons with existing methodologies.