Some correlation tests for vectors of large dimension

Abstract

For a random sample of n iid p-dimensional vectors, each partitioned into b sub-vectors of dimensions p i , i ¼ 1, :::, b, tests for zero correlation of sub-vectors are presented when p i ) n and the distribution need not be normal. The test statistics are composed of U-statistics based estimators of the Frobenius norm measuring the distance between the null and alternative hypotheses. Asymptotic distributions of the tests are provided for n, p i ! 1, with their finite-sample performance demonstrated through simulations. Some related tests are discussed. A real data application is also given.