Question: This and the next two exercises are based on the test statistic usually used to test a set of J linear restrictions in the generalized

This and the next two exercises are based on the test statistic usually used to test a set of J linear restrictions in the generalized regression model: where β is the GLS estimator. Show that if ?? is known, if the disturbances are normally distributed and if the null hypothesis, Rβ = q, is true, then this statistic is exactly distributed as F with J and n ?? K degrees of freedom. What assumptions about the regressors are needed to reach this conclusion? Need they be nonstochastic?

(R$- q)'[R(X'2-X)-R']-(R-q)/J F[J,n-K] = (N XY9-(y X)/(n K)

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First RB q R XNxXN8 q RXNXXN if R q 0 Now use the inverse square root matrix of 2 P 2 to obtain the transformed data X PX 2x y Py 2y and P N Q Q xxxy ... View full answer

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