Exercise 3.9.7 Consider a linear model Y = X + e, E (e) = 0 with the
Question:
Exercise 3.9.7 Consider a linear model Y = Xβ +
e, E
(e) = 0 with the (not necessarily estimable) linear constraint Λ
β =
d. Consider two solutions to the constraint, b1 and b2, so that Λ
bk =
d, k = 1, 2. Define appropriate least squares fitted values Yˆk from the model Y = X0γ + Xbk + e where X0 = XU with C(U) =
C(Λ)
⊥. Show that Yˆ1 = Yˆ2. Hint: After finding Yˆk , show that (I − M0)X(b1 −
b2) = 0.
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