Question: Let (Yi ,Xi ) be a random sample with E[Y j X] X0. Consider theWeighted Least Squares (WLS) estimator ewls X 0W

Let (Yi ,Xi ) be a random sample with E[Y j X] Æ X0¯. Consider theWeighted Least Squares

(WLS) estimator e¯wls Æ

¡

X 0W X

¢¡1 ¡

X 0WY

¢

whereW Æ diag(w1, ...,wn) and wi Æ X¡2 j i , where Xj i is one of the Xi .

(a) In which contexts would e¯wls be a good estimator?

(b) Using your intuition, in which situations do you expect e¯wls to performbetter than OLS?

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