Statistical Inference for High Dimensional Mediation Model
Open Access
- Author:
- Zeng, Mudong
- Graduate Program:
- Statistics
- Degree:
- Doctor of Philosophy
- Document Type:
- Dissertation
- Date of Defense:
- September 28, 2021
- Committee Members:
- Hong Ma, Outside Unit & Field Member
Bing Li, Major Field Member
Zhibiao Zhao, Major Field Member
Runze Li, Chair & Dissertation Advisor
Ephraim Mont Hanks, Program Head/Chair - Keywords:
- Mediation Analysis
Penalized Least Squares
Sparsity - Abstract:
- High-dimensional mediation models (HDMM) draw increasing attention in many scientific areas such as genetic study, clinical trial, and internet analysis. This dissertation is concerned with a new statistical estimation and inference procedure for HDMM, and consists of three projects. In the first project, 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 propose 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 the null hypothesis and a noncentral \chi^2-distribution under local alternatives. Monte Carlo simulations are conducted to examine the finite sample performance of the proposed tests and to compare its performance with existing tests. To illustrate the proposed methodology, we applied the newly proposed statistical inference procedures to study stock reaction to COVID-19 pandemic via an empirical analysis of studying the mediation effects of financial metrics that bridge the company's sector and stock return. In the second project, we conduct a case study by applying high-dimensional linear mediation models. We study the mediating role of DNA methylation relating childhood trauma and cortisol stress reactivity, with several clinical variables involved as confounders. We develop relevant tests for the direct and indirect effects of early life trauma on cortisol stress reactivity. In the third project, as a natural extension of the HDMM, we propose high-dimensional generalized mediation model (HDGMM) to deal with binary or count responses. We propose an estimation procedure for the indirect effects of the models via a partial penalized likelihood method, and further establish its theoretical properties. We also propose a partial penalized Wald test and a partial penalized likelihood ratio test for indirect and direct effects respectively. We show that the proposed test asymptotical distribution under the null hypothesis and local alternatives. Simulation studies are conducted to assess the performance of the estimation and inference procedures for HDGMM. We use HDGMM to classify valuable stocks in COVID-19 pandemic via exploring the underlying mechanism of the relationship between stock market sectors and stock returns.