N ( 0 , A − $^{1}$BA − $^{1}$) with and these expectations are taken with respect to the true parameters ( Θ$_{0}$ , Σ$_{0}$ ) . Without loss of generality we can eliminate the factor 2 Σ − 1 in (17); then it is easy to see that (16) holds. To derive (15) we use differentials again: d {∇ T vec( Θ $_{)}$m$_{(}$ Θ , Σ$_{0}$ $_{)}$( U , V ) } = = 2 ρ $^{′′}$( e ) w $^{2}$( U )( V − Θ $^{T}$U ) $^{T}$Σ − 1 0 (d Θ ) $^{T}$U vec { U ( V − Θ $^{T}$U ) $^{T}$}T + ρ $^{′}$( e ) w ( U )vec { U (d Θ $^{T}$U ) $^{T}$}T = 2 ρ $^{′′}$( e ) w $^{2}$( U )tr { (d Θ ) $^{T}$U ( V − Θ $^{T}$U ) $^{T}$Σ − 1 0 } vec { U ( V − Θ $^{T}$U ) $^{T}$}T + ρ $^{′}$( e ) w ( U )vec( UU $^{T}$d Θ ) T = 2 ρ $^{′′}$( e ) w $^{2}$( U )vec(d Θ ) $^{T}$vec { U ( V − Θ $^{T}$U ) $^{T}$Σ − 1 0 } vec { U ( V − Θ $^{T}$U ) $^{T}$}T + ρ $^{′}$( e ) w ( U ) { ( I$_{q}$ ⊗ UU $^{T}$)vec(d Θ ) } $^{T}$, ∇ vec( Θ ) ∇ T vec( Θ $_{)}$m$_{(}$ Θ , Σ$_{0}$ $_{)}$( U , V ) = so A = E {∇ vec( Θ ) ∇ T vec( Θ $_{)}$m$_{(}$ Θ$_{0}$ , Σ$_{0}$ $_{)}$( U , V ) } B = E {∇ vec( Θ $_{)}$m$_{(}$ Θ$_{0}$ , Σ$_{0}$ $_{)}$( U , V ) ∇ T vec( Θ $_{)}$m$_{(}$ Θ$_{0}$ , Σ$_{0}$ $_{)}$( U , V ) } ; 20