On some exact distribution-free tests of independence between two random vectors of arbitrary dimensions

• Pointed out some limitations of the distribution-free test of independence proposed by Heller et al. (2012)
• Proposed two modified distribution-free tests of independence between two random vectors of arbitrary dimensions.
• These proposed tests are based on traversal of the minimal spanning tree following Prim’s algorithm.
• They are applicable to high dimension, low sample size data.
• They perform well even when the pairwise distances on two random vectors are negatively correlated.

Several nonparametric methods are available in the literature to test the independence between two random vectors. But, many of them perform poorly for high dimensional data and are not applicable when the dimension of one of these vectors exceeds the sample size. Moreover, most of these tests are not distribution-free in the general multivariate set up. Recently, Heller et al. (2012) proposed a test of independence, which is distribution-free and can be conveniently used even when the dimensions are larger than the sample size. In this article, we point out some limitations of this test and propose some modifications to overcome them retaining its distribution-free property. Some simulated and real data sets are analyzed to demonstrate the utility of our proposed modifications.