Abstract
Tests of zero correlation between two or more vectors with large dimension, possibly larger than the sample size, are considered when the data may not necessarily follow a normal distribution. A single-sample case for several vectors is first proposed, which is then extended to the common covariance matrix under the assumption of homogeneity across several independent populations. The test statistics are constructed using a recently proposed modification of the RV coefficient (a correlation coefficient for vector-valued random variables) for high-dimensional vectors. The accuracy of the tests is shown through simulations.
Highlights
Let k = (Xk1, ... , Xkp)T, k = 1, ... , n, be iid random vectors drawn from a population with E ( k) = ∈ Rp and Cov ( k) = ∈ Rp×p, where > 0 can be expressed as a partitioned matrix=i,jb=1 with blocks ij ∈ Rpi×pj, ji = Tij Tii =ii
Consider g ≥ 2 independent populations with lk = (Xlk1, ... , Xlkp)T, k = 1, ... , nl, as iid random vectors drawn from lth population with E = l
We further extend this one-sample multi-block test to a multi-sample case with g independent populations
Summary
N , be iid random vectors drawn from a population with E ( k) = ∈ Rp and Cov ( k) = ∈ Rp×p , where > 0 can be expressed as a partitioned matrix. When the block dimensions, pi , may exceed the sample size, n , and the data may not necessarily follow the multivariate normal distribution. Under H0b , reduces to a block-diagonal structure, = diag( 1, ... Under normality, the test of H0b is equivalent to testing independence of the corresponding vectors. Consider g ≥ 2 independent populations with lk = Nl , as iid random vectors drawn from lth population with E ( lk) = l ,
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