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Proof of Theorem 3.1. As V is p+d+ from Assumption 3+1~d!, VZ T ~ bD ! is p+d+ and invertible w+p+a+1+ Let g~ b! [ E @ g~zt , b!# + Under Assumption 2+1, $ g~zt , b0 !%t` 1 is a stationary and amixing sequence ~White, 1984, Theorem 3+49, p+ 47! and, thus, ergodic ~White, 1984, Proposition 3+44, p+ 46!+ By a uniform weak law of numbers ~Smith, 2001, Lemma A+1!, if Assumptions 2+12+3 and 3+1 hold, supb B 7ST 1 g[ T ~ b! k1 g~ b!7 op~1! and g~ b! is continuous by the strictly stationary and ergodic version of Lemma 2+4 in Newey and McFadden ~1994, p+ 2129!+ Let Q~ b! g~ b!'V 1g~ b!+ Then, by Assumption 3+1~a!, Q ~ b ! is uniquely minimized at b0 and is continuous in b B+ Therefore, as lmin@VZ T ~ bD !# 0 w+p+a+1 where lmin@VZ T ~ bD !# is the smallest eigenvalue of VZ T ~ bD !, uniformly b p+ 2121!+ B+ The result follows by Theorem 2+1 in Newey and McFadden ~1994,