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\begin{eqnarray*} g_1(t) & = & \left\{ \begin{array}{lcl} \ln |\mb{S}_ t| & & \mbox{if the within-group covariance matrices are used} \\ 0 & & \mbox{if the pooled covariance matrix is used} \\ \end{array} \right. \end{eqnarray*}
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