Covariance Structure Tests for t-distribution

We derive expressions of statistics for testing covariance structures when the population is t-distributed. The likelihood ratio test, Rao’s score test and Wald’s score test are derived for basic covariance structures. Expressions of all three statistics are obtained under the general null-hypothesis H01 : Σ = Σ0, using matrix derivative technique. Here p × p-matrix Σ is a dispersion/scale parameter. The special cases H02 : Σ = Ip and H03 : Σ = γ0Ip where γ0 > 0 is a known constant are also considered. Expressions of the statistics are obtained as approximations using first terms from Taylor expansions. The method can be carried over to other continuous multivariate elliptical distributions which have power function in the expression of the density function.