Collaborative Research: Multiple Hypothesis Testing on the Regression Analysis

Temple University, Philadelphia PA

Investigators

Abstract

This research project will develop new theories and methodologies for tackling fundamental issues related to false discovery rate (FDR) control under regression analysis. Novel statistical tools will be provided to analyze data from various scientific studies, such as brain imaging, genome-wide association studies, and atmospheric science. The development of statistical methods to analyze complex data will facilitate discoveries of key variables related to blood pressure, coronary heart disease, stroke, and other critical health issues. Furthermore, this research project will provide training opportunities for graduate students, who will acquire the skills to meet the growing demand for data scientists in industry and academia and software will be developed and made available on publicly accessible websites. Analyzing high-dimensional data using multiple testing under the general framework of regression analysis is a critical challenge in the era of big data. This project will develop a new framework for performing model-free multiple testing for regression analysis, as well as optimal multiple testing for high-dimensional regression model in terms of maximizing the power of detecting the true alternatives subject to the type I error rate control. This framework enables statistical inference for sufficient dimension reduction when the dimension diverges with respect to the sample size and expands the current literature on multiple testing to more complicated data structures where commonly assumed model assumptions are not valid. The framework could also be applied to draw inference for explainable neural networks. The research project not only aims to advance theories in multiple testing but also targets applications of the developed theories. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.