|
Abstract:
|
Researchers are often interested in learning not only the effect of treatments on outcomes, but the pathways through which these effects operate. A mediator is a variable that is affected by treatment and subsequently affects outcome. Existing methods for penalized mediation analyses either assume that finite-dimensional linear models are sufficient to remove confounding bias, or perform no confounding control at all. In practice, these assumptions may not hold. We propose a method that considers the confounding functions as nuisance parameters to be estimated using data-adaptive methods. We then use a novel regularization method applied to this objective function to identify a set of important mediators. We derive the asymptotic properties of our estimator and establish the oracle property under certain assumptions. The local asymptotics of the method are also established, suggesting competitive selection properties. Finally, we propose the perturbation bootstrap for asymptotically valid post-selection inference for the mediated effects of interest. The performance of the proposed method is discussed and theoretical results are corroborated through simulation studies.
|
