In this talk, we will discuss some new insights in the independence tests of high-dimensional data. In the current literature, two sets of test statistics are commonly used for various high-dimensional tests: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. We introduce new testing procedures via distance correlations to boost the power against more general alternatives and retain the correct asymptotic size. Under the high-dimensional setting, we derive the closed-form limiting null distributions, and obtain their explicit rates of uniform convergence. This talk is based on a joint work with Lingzhou Xue at Penn State and Hui Zou at University of Minnesota.
