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First, let us find the mean E $_{p}$γ$_{p}$ , and the variance V $_{p}$γ$_{p}$ of γ$_{p}$ under mea- sure ∏ r j =1 ∏ p i $_{=1}$d P ( j ) pi ( g ( j ) i . Note that V $_{p}$γ$_{p}$ = diag ( V $_{p}$γ (1 , 1) p , V $_{p}$γ (2 , 1) p ,..., V $_{p}$γ ( r,r ) p and E $_{p}$γ$_{p}$ = ( E $_{p}$γ (1 , 1) p , E $_{p}$γ (2 , 1) p ,..., E $_{p}$γ ( r,r ) p ) ′ . With probability one, for sufficiently large p, we have 

which, by Corollary 1, is o (1) uniformly in 2 θ$_{pk}$ ∈ Ω$_{εη}$, a.s.. That Corollary 1 can be applied here follows from the form of expression (7) for K MP p ( x ). Similarly, 

uniformly in 2 θ$_{pk}$, 2 θ$_{ps}$ ∈ Ω$_{εη}$, a.s.. Thus, 

Next, with probability one, for sufficiently large p we have 

Let ˆ H (2) p,ks = ∫ d ˆ F λ p ( λ ) ( K MP p ( 2 θ$_{pk}$ $^{)}$− λ )( K MP p (2 θ$_{ps}$ ) − λ ) and H (2) p,ks = ∫ d F MP p ( λ ) ( K MP p ( 2 θ$_{pk}$ $^{)}$− λ )( K MP p (2 θ$_{ps}$ ) − λ ) . Then, using Corollary 1, we get 

uniformly in 2 θ$_{pk}$, 2 θ$_{ps}$ ∈ Ω$_{εη}$. Similarly, we have p 2 

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and 

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