The variables {Yi ,Xi ,Wi } are a randomsample. The parameter is estimated by minimizing the criterion function S() Xn i1 Wi

The variables {Yi ,Xi ,Wi } are a randomsample. The parameter ¯ is estimated by minimizing the criterion function S(¯) Æ

Xn iÆ1 Wi

¡

Yi ¡X0 i¯

¢2 That is b¯ Æ argmin¯ S(¯).

(a) Find an explicit expression for b¯.

(b) What population parameter ¯ is b¯ estimating? Be explicit about any assumptions you need to impose. Do notmake more assumptions than necessary.

(c) Find the probability limit for b¯ as n!1.

(d) Find the asymptotic distribution of p

n

¡ b¯¡¯

¢

as n!1.