标题：Likelihood ratio test for the hyper-block matrix sphericity covariance structure - characterization of the exact distribution and development of near-exact distributions for the test statistic
摘要：In this paper the authors introduce the hyper-block matrix sphericity test which is a
generalization of both the block-matrix and the block-scalar sphericity tests and as
such also of the common sphericity test. This test is a tool of crucial importance to
verify elaborate assumptions on covariance matrix structures, namely on meta-analysis
and error covariance structures in mixed models and models for longitudinal data. The
authors show how by adequately decomposing the null hypothesis of the hyper-block
matrix sphericity test it is possible to easily obtain the expression for the likelihood
ratio test statistic as well as the expression for its moments. From the factorization
of the exact characteristic function of the logarithm of the statistic, induced by the
decomposition of the null hypothesis, and by adequately replacing some of the factors
with an asymptotic result, it is possible to obtain near-exact distributions that lie very
close to the exact distribution. The performance of these near-exact distributions is
assessed through the use of a measure of proximity between distributions, based on
the corresponding characteristic functions.
