Statistical Inference for Linear Mediation Models with High-Dimensional Mediators

• Activity Number: 364 - Modern Nonparametric Methods, with Applications in Complex Biomedical Data
• Type: Invited
• Date/Time: Wednesday, August 10, 2022 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Runze Li* and Xu Guo and Jingyuan Liu and Mudong Zeng
• Companies: Penn State University and Beijing Normal University and Xiamen University and Penn State University
• Keywords: Mediation Analysis; Penalized Least Squares; Sparsity; Wald test

Abstract

Mediation analysis draws increasing attention in many scientific areas such as genomics. 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 partial penalized least squares method, and further establish its theoretical properties. We further develop a partial penalized Wald test on the indirect effects, and prove that the proposed test has a chi^2 limiting null distribution. We also propose an F-type test for direct effects and show that the proposed test asymptotically follows a chi^2-distribution under null hypothesis and a noncentral chi^2-distribution under local alternatives. We conduct Monte Carlo simulations to examine the finite sample performance of the proposed tests, and illustrate the proposed method by a real data example.