# Changes

$\mathbf{V}=(\mathbf{G}-\bar{\mathbf{G}})^T (\hat{\boldsymbol{\Omega}}^{-1}-\hat{\boldsymbol{\Omega}}^{-1} \mathbf{X}(\mathbf{X^T}\hat{\boldsymbol{\Omega}}^{-1}\mathbf{X})^{-1} \mathbf{X^T} \hat{\boldsymbol{\Omega}}^{-1})(\mathbf{G}-\bar{\mathbf{G}})$.
Under the null, The score test statistics statistic $T_i=(U_i^2)/V_{ii}$ is asymptotically distributed as chi-squared with one degree of freedom.