Power Boosting: Fusion of Multiple Test Statistics via Resampling
Efang Kong, Yü Liu, Yingcun Xia · Statistica Sinica · 2023
For the same null hypothesis, there usually exist multiple valid test statistics.In nearly all cases, any individual statistic is only powerful against specific types of alternatives, and could be rather weak in picking up signals of other types.It is thus crucial, especially in highdimensional settings, to combine the information contained in different test statistics in order to maintain robust power against a wide range of alternatives, thus avoiding the worst-case scenario.Methods have been proposed for similar purposes, but they are either computationally expensive or lack theoretical justification.In this paper, we present a general and easy-to-implement procedure for fusing multiple valid statistics through resampling methods such as bootstrap or permutation.The consistency of this procedure is proved for three popular high-dimensional hypothesis testing problems.Intensive numerical studies show that this fusion procedure maintains robust performances against a wide range of alternatives, while individual test statistics would often suffer from extremely low power.