Adaptive testing for association between two random vectors in moderate to high dimensions - Xu, Zhiyuan (Genet Epidemiol, 2017)
Testing for association between two random vectors is a common and important task in many fields, however, existing tests, such as Escoufier’s RV test, are suitable only for low-dimensional data, not for high-dimensional data. In moderate to high dimensions, it is necessary to consider sparse signals, which are often expected with only a few, but not many, variables associated with each other. We generalize the RV test to moderate to high dimensions. The key idea is to data-adaptively weight each variable pair based on its empirical association. As the consequence, the proposed test is adaptive, alleviating the effects of noise accumulation in high-dimensional data, and thus maintaining the power for both dense and sparse alternative hypotheses. We show the connections between the proposed test with several existing tests, such as a generalized estimating equationsG-based adaptive test, multivariate kernel machine regression, and kernel distance methods. Furthermore, we modify the proposed adaptive test so that it can be powerful for non-linear or non-monotonic associations. We use both real data and simulated data to demonstrate the advantages and usefulness of the proposed new test. The new test is freely available in R package aSPC at https://github.com/jasonzyx/aSPC.