  Testing a global null is a canonical problem in statistics and has a wide
range of applications. In view of the fact that no uniformly most powerful test
exists, prior and/or domain knowledge are commonly used to focus on a certain
class of alternatives to improve the testing power. 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 for
global nulls. We 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 and an analysis of a real WGS dataset are
conducted to demonstrate the type I error control and/or power gain of the
proposed ensemble tests.
