The expression for the restricted coefficient vector in (523) may be written in the form b =[I
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The expression for the restricted coefficient vector in (523) may be written in the form b∗ =[I − CR]b + w, where w does not involve b. What is C? Show that the covariance matrix of the restricted least squares estimator is
σ^{2}(X'X)^{−1} − σ^{2}(X'X)^{−1 }R'[R(X'X)^{−1}R']^{−1}R(X'X)^{−1}
and that this matrix may be written as
Var[b X] {[Var(b X)]^{−1} − R'[Var(Rb) X]^{−1}R} Var[b X].
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By factoring the result in 5 23 we obtain b I CR b w ...View the full answer
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