content_image/321684.jpg content_image/321685.jpg content_image/321686.jpg content_image/321687.jpg
<img src='content_image/321684.jpg'>

Finally, using the Law of Large Numbers, (A.40) and (A.41) we get (A.35) and this proves (A.30). ■ 

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 

<img src='content_image/321685.jpg'>

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 

<img src='content_image/321686.jpg'>

Proof: To prove the Lemma it suffices to show that for any ε > 0 there exists η > 0 such that 

<img src='content_image/321687.jpg'>

