The Wald test statistic in (6) for θ = ˆ θ$_{T}$, λ = λ$_{T}$, Ω = ˆ V$_{T}$ and with y$_{T}$ = A ( ˆ θ$_{T}$ − ¯ θ ) can be written as Consider g ¯ θ, $_{0}$( y ) for A$_{0}$ = V − 1 2 , and g ¯ θ, $_{1}$( y ) for some nonsingular A ; then the distribution of g ¯ θ, $_{1}$( V 1 2 AZ ) is the same as g ¯ θ, $_{0}$( Z ) . The distribution of G ¯ θ, $_{1}$( V 1 2 AZ ) is the same as G ¯ θ, $_{0}$( Z ) V − 1 2 A − $^{1}$, since we consider non-singular reparametrizations of continuous functions. Thus the limit distribution does not depend on A. Below we write g ¯ $_{θ}$, G ¯ θ for g ¯ θ, 0 and G ¯ θ, $_{0}$. Theorem 4.1. Under the Assumptions 2.1a, 2.2, 2.3 and 2.4 if (a) at ¯ θ the CLDR property holds for G ¯ $_{θ}$( y ) (for any non-singular A ) then the limit distribution of W$_{T}$ as T → ∞ is given by the distribution of if (b) at ¯ θ the deficient rank property holds, then W$_{T}$ diverges to infinity as T → ∞ . Corollary 4.1. When the CLDR property holds the limit distribution can be represented as the distribution of Z $^{′}$[ ¯ G ¯ $_{θ}$( Z )] $^{′}$Λ ¯ θ {[ ¯ G ¯ $_{θ}$( Z ) ] [ ¯ G ¯ $_{θ}$( Z )] $^{′}$} − $^{1}$Λ ¯ $_{θ}$[ ¯ G ¯ $_{θ}$( Z )] Z. (26) This follows from the Euler formula (19) . [¯ g ¯ $_{θ}$( Z )] $^{′}${[ ¯ G ¯ $_{θ}$( Z ) ] [ ¯ G ¯ $_{θ}$( Z )] $^{′}$} − $^{1}$[¯ g ¯ $_{θ}$( Z )]; (25) λ 2 $_{T}$g ′ ¯ $_{θ}$( y$_{T}$ )[ G ¯ $_{θ}$( y$_{T}$ ) A ˆ V$_{T}$A $^{′}$G′ ¯ $_{θ}$( y$_{T}$ )] − $^{1}$g ¯ $_{θ}$( y$_{T}$ ) . 26