inf ‖ B ‖ 2 >L 2 1 n n ∑ i =1 ρ$_{1}$ ( d$_{i}$ ( B , ̂ Γ$_{n}$ ) σ ) ≥ inf ‖ B ‖ 2 >L 2 1 n n ∑ i =1 ρ$_{1}$ ( ‖ y$_{i}$ − B $^{′}$x ‖ L 1 / 2 1 σ ) ≥ inf ‖ B ‖ 2 =1 1 n n ∑ i =1 ρ$_{1}$ ( ‖ y$_{i}$ ‖ − L$_{2}$ϕ L 1 / 2 1 σ ) I ( ‖ B $^{′}$x ‖ > ϕ ) I ( ‖ y$_{i}$ ‖ < L$_{2}$ϕ ) ≥ inf 1 ≤ j ≤ s inf B ∈ C j 1 n n ∑ i =1 ρ$_{1}$ ( ‖ y$_{i}$ ‖ − M L 1 / 2 1 σ ) I ( ‖ B $^{′}$x ‖ > ϕ ) I ( ‖ y$_{i}$ ‖ < M ) ≥ inf 1 ≤ j ≤ s 1 n n ∑ i =1 inf B ∈ C j ρ$_{1}$ ‖ y$_{i}$ ‖ − M L 1 / 2 1 σ I ( ‖ B $^{′}$x ‖ > ϕ )(1 − I ( ‖ y$_{i}$ ‖ ≥ M )) E$_{Q}$ ( sup ‖| ( A , V ) − ( A$_{0}$ , V$_{0}$ ) ‖|≤ δ | g ( z , ( A , V )) | ) < ∞ , lim n $_{−→∞}$(1 /n ) n ∑ i =1 g ( z$_{i}$ , ( ̂ A$_{n}$ , ̂ V$_{n}$ )) = E$_{Q}$ g ( z , ( A$_{0}$ , V$_{0}$ )) a.s .. lim$_{n}$$_{−→∞}$ sup ‖| ( A , V ) − ( A$_{0}$ , V$_{0}$ ) ‖|≤ η (1 /n ) n ∑ i =1 g ( z$_{i}$ , ( A , V )) ≤ E$_{Q}$ g ( z , ( A$_{0}$ , V$_{0}$ ))+ ε (A.42) 48 Proof: To prove the Lemma it suffices to show that for any ε > 0 there exists η > 0 such that where ‖| · ‖| is the norm defined in (A.5) . Let ( ̂ A$_{n}$ , ̂ V$_{n}$ ) be a sequence of estimates in R m × n × R r × t such that lim$_{n}$$_{−→∞}$( ̂ A$_{n}$ , ̂ V$_{n}$ ) = ( A$_{0}$ , V$_{0}$ ) a.s.. Then if z$_{1}$ , . . . , z$_{n}$ , are i.i.d. random variables in R k with distribution Q , we have Lemma 17. Let g : R k × ( R m × n × R r × $^{t}$) −→ R continuous and let Q be a probability distribution on R k such that for some δ > 0 we have Finally, using the Law of Large Numbers, (A.40) and (A.41) we get (A.35) and this proves (A.30). ■