The Penn State University
(Colloquium Tea held at 4:00 pm in 101A Crowley Hall)
Statistical Inference for Linear Mediation Models with High-dimensional Mediators
Mediation analysis draws increasing attention in many research areas such as economics, finance, social sciences studies and genetic studies. In this paper, we propose new statistical inference procedures for high dimensional mediation models, in which both the outcome model and the mediator model are linear with high dimensional mediators. Traditional procedures for mediation analysis cannot be used to make statistical inference for high dimensional linear mediation models due to high-dimensionality of the mediators. We propose an estimation procedure for the indirect effects of the models via a partially penalized least squares method, and further establish its theoretical properties. We further develop a partially penalized Wald test on the indirect effects, and prove that the proposed test has a chi-square limiting null distribution. We also propose an F-type test for direct effects and show that the proposed test asymptotically follows a chi-square distribution under null hypothesis and a noncentral chi-square distribution under local alternatives. We conduct numerical studies to assess the finite sample performance of the proposed methods, and empirical analysis to illustrate the proposed methodology.