content_image/303416.jpg content_image/303415.jpg content_image/303414.jpg
Using a suitable change of variables, for all Σ ∈ S q we have that 

<img src='content_image/303416.jpg'>

Since this holds for all k = 1 , . . . , q and j = 1 , . . . , p so that 

for all Σ ∈ S $_{q}$. 

By (2.10), the pair θ$_{n}$ = ( ̂ B$_{n}$ , ̂ Σ$_{n}$ ) is a zero of the function (1 /n ) ∑ n i $_{=1}$φ ( z$_{i}$ , θ ). Using this, after doing some simple operations of sum and subtraction and using (A.55), we have 

<img src='content_image/303415.jpg'>

<img src='content_image/303414.jpg'>

Since E$_{H}$$_{0}$φ ( z , θ$_{n}$ ) is equal to Φ( ̂ B$_{n}$ , ̂ Σ$_{n}$ ), we can solve for E$_{H}$$_{0}$φ ( z , θ$_{n}$ ) in the 

