Distinguished Lecture: Ensemble Methods for Testing a Global Null with Applications in Whole Genome Sequencing Studies

Abstract: Testing a global null is a canonical problem in statistics and has a wide range of applications. In view of the fact of no uniformly most powerful test, prior and/or domain knowledge are commonly used to focus on a certain class of alternatives to improve the testing power, e.g., the class of alternatives in the scenario of the same effect sign or signal sparsity. However, it is generally challenging to develop tests that are particularly powerful against a certain class of alternatives. In this paper, motivated by the success of ensemble learning methods for prediction or classification, we propose an ensemble framework for testing that mimics the spirit of random forests to deal with the challenges. Our ensemble testing framework aggregates a collection of weak base tests to form a final ensemble test that maintains strong and robust power. The key component of the framework is to introduce a certain random procedure in the construction of base tests. We then apply the framework to four problems about global testing in different classes of alternatives arising from Whole Genome Sequencing (WGS) association studies. Specific ensemble tests are proposed for each of these problems, and their theoretical optimality is established in terms of Bahadur efficiency. Extensive simulations are conducted to demonstrate type I error control and power gain of the proposed ensemble tests. In an analysis of the WGS data from the Atherosclerosis Risk in Communities (ARIC) study, the ensemble tests demonstrate substantial and consistent power improvement compared to other existing tests. This is a joint work with Yaowu Liu (Southwestern Financial University) and Zhonghua Liu (Columbia University).