Consider now the original matrix G ( y ) , denote it G $^{1}$( y ) with q$_{1}$ = q and employ the construction recursively until for some m it ends: Σ m v $_{=1}$¯ r$_{v}$ = q. Denote by ¯ S v the matrix    I$_{¯}$ r$_{1}$ + ... +¯ r$_{v}$$_{−}$$_{1}$ S v    and define S = ¯ S $^{m}$... ¯ S $^{1}$. Set a = ( α$_{1}$, ..., α$_{q}$ ) = ( ¯ k$_{1}$, ..., ¯ k$_{1}$, ..., ¯ k$_{m}$, ..., ¯ k$_{m}$ ) , where each ¯ k$_{v}$ enters ¯ r$_{v}$ times. Then for this a and S From Assumption 2.3 if λ = λ$_{T}$ and θ = ˆ θ$_{T}$ then the probability limit of corresponding V − 1 2 A − $^{1}$y ∗ T is Z with distribution Q ( ¯ θ ) ; from Assumption 2.4 ˆ V$_{T}$ = V + o$_{p}$ (1) . From (20) and convergence it follows that is a finite matrix ¯ G ( y ) =    ¯ G $^{1}$( y ) . ¯ G $^{m}$( y )   $^{; if}$ q ∑ i =1 α$_{i}$ = ¯ α, then CLDR property q holds, if ∑ i =1 α$_{i}$ < ¯ α then the limit matrix has deficient rank. Proof of Theorem 4.1. Consider y ∗ = λ$_{T}$ y$_{T}$ Proof of Theorem 4.1. Consider y T = λ$_{T}$ y$_{T}$ and the quadratic form similar to (21) W ( y ∗ $_{T}$, g ¯ $_{θ}$, λ$_{T}$ , A ˆ V$_{T}$ A $^{′}$) = λ 2 $_{T}$g ′ ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ )[ G ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ ) A ˆ V$_{T}$ A $^{′}$G′ ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ )] − $^{1}$g ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ ) . lim λ $_{→∞}$[ diag ( λ $^{α$_{i}$}$) SG ( y/λ )] diag ( λ α$_{i}$ T ) SG ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ ) = ¯ G ¯ $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ ); (32) diag ( λ α$_{i}$ T ) Sλg ¯ $_{θ}$( y ∗ $_{T}$/λ$_{T}$ ) = ¯ g $_{θ}$( y ∗ $_{T}$) + O$_{p}$ (1 /λ$_{T}$ ) . 42