A test for block circular symmetric covariance structure with divergent dimension

Abstract

The paper considers the likelihood ratio (LR) test on the block circular symmetric covariance structure of a multivariate Gaussian population with divergent dimension. When the sample sizen, the dimension of each blockpand the number of blocksusatisfypu<n− 1 andp=p(n) →∞asn→∞, the asymptotic distribution and the moderate deviation principle of the logarithmic LR test statistic under the null hypothesis are established. Some numerical simulations indicate that the proposed LR test method performs well in the divergent-dimensional block circular symmetric covariance structure test.