and From Assumption (iii) we know are all finite non-zero, Slutsky’s theorem implies which is finite and invertible. (c) The conditional expectation The second equality used Assumption (ii) that are i.i.d., and the third equality applied the conditional mean independence assumption (i). (d) In the limit because (e) converges in probability to a finite invertible matrix, and converges in probability to a zero vector. Applying Slutsky’s theorem, This implies   18.11. (a) Using the hint C [Q1 Q2], where QQ I. The result follows with AQ1.   (b) W AV N(A0, AInA) and the result follows immediately.    (c) VCV VAAV (AV)(AV) W’W and the result follows from (b). 18.13. (a) This follows from the definition of the Lagrangian.
and From Assumption (iii) we know are all finite non-zero, Slutsky’s theorem implies which is finite and invertible. (c) The conditional expectation The second equality used Assumption (ii) that are i.i.d., and the third equality applied the conditional mean independence assumption (i). (d) In the limit because (e) converges in probability to a finite invertible matrix, and converges in probability to a zero vector. Applying Slutsky’s theorem, This implies 18.11. (a) Using the hint C  [Q1 Q2], where QQ  I. The result follows with AQ1. (b) W  AV  N(A0, AInA) and the result follows immediately. (c) VCV  VAAV  (AV)(AV)  W’W and the result follows from (b). 18.13. (a) This follows from the definition of the Lagrangian.