For one restriction CLDR always holds and ˆ a = ˆ k as defined in Lemma 6.2 provides α with probability approaching 1. For several restrictions estimate ˆ k$_{det}$, ˆ G ¯ $_{θ}$( y ) as defined in Theorem 6.1. and then if CLDR property holds it is sufficient to define the estimate of α as the smallest diagonal element of ˆ Λ ¯ θ as in Theorem 6.1. This estimator will equal the true α with probability approaching 1. Use the bound 1 (ˆ a +1) 2 χ 2 $_{p}$. Proof of lemma 4.1. We first note that for the submatrix ˜ G$_{l}$ ( y ) defined by (13), is a submatrix of ¯ G ( y ) . Then exists and since S is nonsingular Then this is lim λ → + $_{$_{∞}$λ}$∑ q i $_{=1}$α$_{i}$ det( ˜ G$_{l}$ ( y/λ )) < ∞ . lim λ → + ∞ ( $_{λ}$∑ q i $_{=1}$α$_{i}$ − ¯ a ) λ ¯ $^{a}$det( ˜ G$_{l}$ ( y/λ )) lim λ → + $_{$_{∞}$λ}$∑ q i $_{=1}$α$_{i}$ det( S ) det( ˜ G$_{l}$ ( y/λ )) ¯ G$_{l}$ ( y ) = lim λ =+ $_{∞}$diag ( λ $^{α$_{i}$}$) S ˜ G$_{l}$ ( y/λ ) 7 Appendix: Proofs 39