diag ( λ $^{α$_{i}$}$) SG ( y/λ ) = ¯ G ( y ) + O (1 /λ ); (20) diag ( λ $^{α$_{i}$}$) Sλg ( y/λ ) = ¯ g ( y ) + O (1 /λ ) . W ( y, g, λ, Ω) = λ $^{2}$g $^{′}$( y/λ )[ G ( y/λ )Ω G $^{′}$( y/λ )] − $^{1}$g ( y/λ ) . (21) W ( y, g, λ, Ω) = g $^{′}$( y/λ ) λS $^{′}$( λ )[ S ( λ ) G ( y/λ )Ω G $^{′}$( y/λ ) S $^{′}$( λ )] − $^{1}$S ( λ ) λg ( y/λ ) . (22) W ( y, g, λ, Ω) = [¯ g ( y ) + O (1 /λ )] ′ { [ ¯ G ( y ) + O (1 /λ ) ] [Ω 0 + o (1)] [ ¯ G ( y ) + O (1 /λ ) ] ′ } − $^{1}$[¯ g ( y ) + O (1 /λ )] . Suppose that Ω = Ω ( λ ) with the property that as λ → ∞ the matrix Ω = Ω $^{0}$+ o (1) , with Ω 0 a non-singular matrix. Then we can write as λ → ∞ If CLDR property holds for G, ¯ G ( y ) is full rank and then 23 Define now for some positive definite matrix Ω a quadratic form Note that W ( y, g, λ, Ω) = W ( y, Mg, λ, Ω) for any non-singular matrix M ; we can choose M = S ( λ ) = diag ( λ $^{α$_{i}$}$) S. This provides