Abstract: In the current literature, two sets of test statistics are commonly used for high-dimensional hypothesis testing: 1) using extreme-value form statistics to test against sparse alternatives, and 2) using quadratic form statistics to test against dense alternatives. However, quadratic form statistics suffer from low power against sparse alternatives, and extreme-value form statistics suffer from low power against dense alternatives with small disturbances and may have size distortions due to its slow convergence. For real-world applications, it is important to derive powerful testing procedures against more general alternatives. Based on their joint limiting laws, we introduce a new general power enhancement testing procedure to boost the power against more general alternatives and retain the correct asymptotic size. In the high-dimensional setting, we derive the closed-form limiting null distributions, and obtain their explicit rates of uniform convergence. The proposed power enhancement test is demonstrated in various parametric and nonparametric tests for high-dimensional means, banded covariances, spiked covariances, and so on. We demonstrate the finite-sample performance of our proposed testing procedures in both simulation studies and real applications.
Short Bio: Lingzhou Xue is currently an Assistant Professor of Statistics at The Pennsylvania State University. He received his B.S. degree in Statistics from Peking University in 2008 and Ph.D. degree in Statistics from University of Minnesota in 2012. He was a postdoctoral research associate at Princeton University before joining Penn State. His research interests include the convex/nonconvex statistical learning, high-dimensional statistical inference, large-scale graphical models, dynamic network models, and high-dimensional nonparametric/semiparametric statistics.