Take the projection model Y X0e with E Xe 0 For a positive function w(x) let Wi w(Xi ) Consider the estimator e Xn i1 Wi Xi X0 i 1 Xn i1 Wi XiYi Find the probability limit (as n 1) of e Do you need to add an assumption Is e consistent for e If not, under what assumption is e consistent for

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Question: Take the projection model Y X0e with E[Xe] 0. For a positive function w(x) let Wi w(Xi ). Consider the estimator e

Take the projection model Y Æ X0¯Åe with E[Xe] Æ 0. For a positive function w(x) let Wi Æ w(Xi ). Consider the estimator e¯ Æ

Xn iÆ1 Wi Xi X0 i

!¡1 Ã

Xn iÆ1 Wi XiYi

Find the probability limit (as n !1) of e¯. Do you need to add an assumption? Is e¯ consistent for e¯? If not, under what assumption is e¯ consistent for ¯?

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