Then W ( y ∗ $_{T}$,g ¯ $_{θ}$,λ$_{T}$ ,A ˆ V$_{T}$A $^{′}$) = substituting the reparametrized functions for A = V − 1 2 we get the result. (b) Follows by continuity of the determinants of polynomial matrices and (24) . (a) If CLDR holds then W$_{T}$ by continuity of the determinants of polyno- mials and polynomial matrices converges to Proof of Theorem 5.1. Consider the asymptotically equivalent statistic: Z ′ ¯ G ( Z ) $^{′}$Λ [ ¯ G ( Z ) ¯ G ( Z ) $^{′}$] − 1 Λ ¯ G ( Z ) Z = Z ′ ¯ G ( Z ) ′ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 × [ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) 1 2 Λ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 Λ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) 1 2 ] × ( ¯ G ( Z ) ¯ G ( Z ) − 1 2 ¯ G Z ) Z ≤ ∥ ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 ¯ G ( Z ) Z ∥ ∥$^{2}$ ∥ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) 1 2 Λ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 ∥ × ∥ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) − 1 2 Λ ( ¯ G ( Z ) ¯ G ( Z ) $^{′}$) 1 2 ∥ ≤ ‖ Λ ‖ 2 ‖ Z ‖ 2 ∼ 1 (1 + i$_{0}$ ) $_{2}$χ 2 $_{p}$, [¯ g ¯ $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ )] ′ { [ ¯ G ¯ $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ ) ] A [ V + o$_{p}$ (1)] A ′ [ ¯ G ¯ $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ ) ] ′ } − 1 × [¯ g ¯ $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ )] . [¯ g ¯ $_{θ}$( Z )] ′ { [ ¯ G ¯ $_{θ}$( Z )] AV A $^{′}$[ ¯ G ¯ $_{θ}$( Z )] $^{′}$} − 1 [¯ g ¯ $_{θ}$( Z )]; 43