This paper proposes the corrected likelihood ratio test(LRT) and large-dimensional trace criterion to test the independence of two large sets of multivariate variables of dimensions p1 and p2 when the dimensions p=p1+p2 and the sample size n tend to infinity simultaneously and proportionally.Both theoretical and simulation results demonstrate that the traditional χ2 approximation of the LRT performs poorly when the dimension p is large relative to the sample size n,while the corrected LRT and large-dimensional trace criterion behave well when the dimension is either small or large relative to the sample size.Moreover,the trace criterion can be used in the case of p> n,while the corrected LRT is unfeasible due to the loss of definition.
