\begin{array} { r l r } & { } & { L _ { 4 } ^ { \ast } \underset { n \longrightarrow \infty } { \overset { \mathcal { P } } { \longrightarrow } } \frac { \tau + 1 } { \left( 2 \pi \right) ^ { m \tau / 2 } } \frac { \tau } { 4 } \left\vert \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) \right\vert ^ { - \frac { \tau } { 2 } } \frac { 1 } { \left( 1 + \tau \right) ^ { m / 2 } } } \\ & { } & { \left\{ t r a c e \left\{ \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { j } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \right) \left[ \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } + \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \right] \right. \right. } \\ & { } & { \left. \left. \frac { \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { 1 + \tau } \right\} + t r a c e \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { 1 + \tau } \right) t r a c e \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { 1 + \tau } \right) \right\} } \\ & { } & { = 2 \frac { \tau } { 4 } \frac { \left\vert \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) \right\vert ^ { - \frac { \tau } { 2 } } } { \left( 2 \pi \right) ^ { m \tau / 2 } } \frac { 1 } { \left( 1 + \tau \right) ^ { m / 2 + 1 } } t r a c e \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \right) } \\ & { } & { + \frac { \tau } { 4 } \frac { \left\vert \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) \right\vert ^ { - \frac { \tau } { 2 } } } { \left( 2 \pi \right) ^ { m \tau / 2 } } \frac { 1 } { \left( 1 + \tau \right) ^ { m / 2 + 1 } } t r a c e \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { j } } \right) t r a c e \left( \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) ^ { - 1 } \frac { \partial \boldsymbol { \Sigma } \left( \boldsymbol { \theta } \right) } { \partial \theta _ { i } } \right) . } \end{array}