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, 11:43, 11 March 2014
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| We further derive the variance-covariance matrix of these statistics as | | We further derive the variance-covariance matrix of these statistics as |
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− | <math> \mathbf{V}=(\mathbf{G}-\bar{\mathbf{G}})^T (\boldsymbol{\Omega}^(-1)-\boldsymbol{\Omega}^(-1) \mathbf{X}(\mathbf{X^T}\boldsymbol{\Omega}^(-1)\mathbf{X})^(-1) \mathbf{X^T} \boldsymbol{\Omega}^(-1))(\mathbf{G}-\bar{\mathbf{G}}) </math>.
| + | <math> \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}}) </math>. |
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| Under the null, test statistics T_i=(U_i^2)/V_ii is asymptotically distributed as chi-squared with one degree of freedom. | | Under the null, test statistics T_i=(U_i^2)/V_ii is asymptotically distributed as chi-squared with one degree of freedom. |