where δ$_{js}$ = 1 { j = s } stands for the classical Kronecker symbol. As will be shown below, after an appropriate change of measure, γ ( j,s ) p 1 and γ ( j,s ) p 2 are asymptotically centered Gaussian. Expressing the exponent in (22) as a function of γ ( j,s ) p 1 and γ ( j,s ) p 2 , changing the measure of integration, and using the asymptotic Gaussianity will establish the proposition. Let γ$_{p}$ = ( γ (1 , 1) p , ..., γ ( r, 1) p , γ (2 , 2) p , ..., γ ( r, 2) p , γ (3 , 3) p , ..., γ ( r,r ) p ′$_{, where}$ γ ( j,s ) p = ( γ ( j,s ) p 1 , γ ( j,s ) p 2 ) . Using this notation, (22), (23), and (24), we get, after some algebra, where P is the standard Gaussian probability measure, and where G ( j ) pi is a ( j − 1) × ( j − 1) matrix with ( k, s )-th element p − 1 / $^{2}$γ ( k,s ) pi , Next, define the event B$_{M,M}$$_{′}$ = {∣ ∣ γ ( j,s ) p 1 ∣ ≤ M and ∣ γ ( j,s ) p 2 ∣ ≤ $_{M}$′ for all j, s = 1 , ..., r } , where M and M ′ are positive parameters to be specified later. Somewhat abusing notation, we will also refer to B$_{M,M}$$_{′}$ as a rectangular region in R r $^{2}$+ r that consists W$_{pj}$ = diag ( v$_{p}$$_{1}$$^{, ..., v$_{p,j}$}$− $_{1}$) , and γ ( j, 1: j − 1) pi = ( γ ( j, 1) pi , ..., γ ( j,j − 1) pi ) ′ . f$_{p,θ}$ ( γ$_{p}$ ) = exp { r ∑ j =1 θ$_{pj}$ N$_{1}$$_{j}$ + ... + N$_{6}$$_{j}$ D$_{j}$ } with (26) N$_{1}$$_{j}$ = − γ ( j,j ) p 1 ( γ ( j,j ) p 2 − v$_{pj}$γ ( j,j ) p 1 ) , N$_{2}$$_{j}$ = γ ( j, 1: j − 1) ′ p 1 ( G ( j ) p 1 + I ) − 1 ( G ( j ) p 2 + W$_{pj}$ ) ( G ( j ) p 1 + I ) − 1 γ ( j, 1: j − 1) p 1 , N$_{3}$$_{j}$ = − 2 γ ( j, 1: j − 1) ′ p 1 ( G ( j ) p 1 + I ) − 1 γ ( j, 1: j − 1) p 2 , N$_{4}$$_{j}$ = v$_{pj}$γ ( j, 1: j − 1) ′ p 1 G ( j ) p 1 + I − 1 γ ( j, 1: j − 1) p 1 , N$_{5}$$_{j}$ = $_{p}$− 1 / $^{2}$γ ( j,j ) p 2 γ ( j, 1: j − 1) ′ p 1 ( G ( j ) p 1 + I ) − 1 γ ( j, 1: j − 1) p 1 , N$_{6}$$_{j}$ = − $_{p}$− 1 / $^{2}$v$_{pj}$ γ (1: j − 1 ,j ) ′ p 1 G ( j ) p 1 + I − 1 γ (1: j − 1 ,j ) p 1 γ ( j,j ) p 1 , and D$_{j}$ = 1 + $_{p}$− 1 / $^{2}$γ ( j,j ) p 1 − $_{p}$− $^{1}$γ ( j, 1: j − 1) ′ p 1 ( G ( j ) p 1 + I ) − 1 γ ( j, 1: j − 1) p 1 , I$_{p}$ (Θ$_{p}$ , Λ$_{p}$)= ∫ f$_{p,θ}$ ( γ$_{p}$ ) e p ∑ r j =1 θ$_{pj}$ ( v$_{pj}$ +ˆ γ ( j,j ) p − v$_{pj}$γ ( j,j ) p ) r ∏ j =1 p ∏ i =1 d P ( g ( j ) i ) , (25) 24