entiable function of ω , √$_{I}$$_{(}$ ˆ h$_{z}$ − h$_{z}$ ) D −→ N ( 0 , { ∂h$_{z}$/∂ ω } T F − $^{1}${ ∂h$_{z}$/∂ ω } ) with and The asymptotic variance of ˆ h$_{z}$ is then given by The asymptotic distribution of (11) is derived in a similar way. If ζ = (diag( Σ ) , diag( Ω )) , $_{then}$√$_{I}$$_{(}$ ˆ ζ − ζ ) D −→ N ( 0 , G − $^{1}$) with G = E[ { ∂ ∂ ζ log f ( y$_{i}$$_{·}$ ) }{ ∂ ∂ ζ log f ( y$_{i}$$_{·}$ ) } $^{T}$] $_{, and}$√$_{I}$$_{(}$ ˆ h$_{w}$ − h$_{w}$ ) D −→ N (0 , avar( ˆ h$_{w}$ )) with avar( ˆ h$_{w}$ ) = ( ∂h$_{w}$/∂ ζ ) T G − $^{1}$( ∂h$_{w}$/∂ ζ ) , where and ∂h$_{w}$ ∂ Σ$_{kk}$ = tr( Ω ) { tr( Σ ) + tr( Ω ) } $_{2}$, for k = 1 , . . . , r, ∂h$_{w}$ ∂ Ω$_{kk}$ = − tr( Σ ) { tr( Σ ) + tr( Ω ) } $_{2}$, for k = 1 , . . . , r. avar( ˆ h$_{z}$ ) = ( ∑ p k $_{=1}$λ$_{k}$ ) 2 ( ∑ p k $_{=1}$γ$_{k}$ + ∑ q k $_{=1}$λ$_{k}$ ) 4 · p ∑ k =1 p ∑ l =1 ( F − 1 ) kl − 2 ( ∑ p k $_{=1}$γ$_{k}$ ) ( ∑ q k $_{=1}$λ$_{k}$ ) ( p k $_{=1}$γ$_{k}$ + q k $_{=1}$λ$_{k}$ ) 4 · p ∑ k =1 q ∑ l =1 ( F − 1 ) k,p + l + ( ∑ q k $_{=1}$γ$_{k}$ ) 2 ( ∑ p k $_{=1}$γ$_{k}$ + ∑ q k $_{=1}$λ$_{k}$ ) 4 · q ∑ k =1 q ∑ l =1 ( F − 1 ) p + k,p + l . ∂h$_{z}$ ∂γ$_{k}$ = ∑ q k $_{=1}$λ$_{k}$ ( ∑ p k $_{=1}$γ$_{k}$ + ∑ q k $_{=1}$λ$_{k}$ ) $_{2}$, k = 1 , . . . , p, ∂h$_{z}$ ∂λ$_{k}$ = − ∑ p k $_{=1}$γ$_{k}$ ( ∑ p k $_{=1}$γ$_{k}$ + ∑ q k $_{=1}$λ$_{k}$ ) $_{2}$, k = 1 , . . . , q. 13