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

F[J, n K] = (RB q)'[R(X'Q-'X)-'R']-'(R q)/J (y XBY2'(y X,)/(n K)

where β̂ is the GLS estimator. Show that if Ω 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?

F[J, n K] = (RB q)'[R(X'Q-'X)-'R']-'(R q)/J (y XBY2'(y X,)/(n K)

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