B0859
Title: A general approach for testing independence in Hilbert spaces
Authors: Daniel Gaigall - FH Aachen University of Applied Sciences (Germany) [presenting]
Shunyao Wu - Qingdao University (China)
Hua Liang - George Washington University (United States)
Abstract: The projection correlation idea is generalized for testing the independence of random vectors, which is known as a powerful method in multivariate analysis. For covering infinite-dimensional situations, a universal Hilbert space approach is chosen. It is proven that the new tests keep the significance level under the null hypothesis of independence and can detect any alternative of dependence in the limit. Simulations demonstrate that the generalization does not impair the good performance of the approach. Furthermore, extended and new limit results in high dimensional cases where the sample size and simultaneously the dimension of the observations tend to infinity are established. Additional simulations confirm the theoretical findings. Furthermore, the implementation of the new approach is described and presented as a real data example for illustration.
