content_image/309244.jpg content_image/309245.jpg content_image/309247.jpg content_image/309249.jpg content_image/309246.jpg content_image/309248.jpg
and (11) follows. Differentiating m with respect to Σ we obtain 

<img src='content_image/309244.jpg'>

<img src='content_image/309245.jpg'>

so 

Again, this can be expressed in matrix form as 

from which (12) follows. 

<img src='content_image/309247.jpg'>

<img src='content_image/309249.jpg'>

<img src='content_image/309246.jpg'>

<img src='content_image/309248.jpg'>

We will simplify the derivation of the asymptotic distribution of ˆ Θ by assuming that the true component scores ( U$_{i}$ , V$_{i}$ ) are used, instead of the estimated scores ( ˆ U$_{i}$ , ˆ V$_{i}$ ) , and by assuming that Σ$_{0}$ is fixed and known. In that case we can apply Theorem 5.23 of Van der Vaart (1998) directly, and obtain that √$_{n}$ { vec( ˆ Θ ) − vec( Θ$_{0}$ ) } is asymptotically 

