Testing Many Restrictions Under Heteroskedasticity
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We propose a hypothesis test that allows for many tested restrictions in a heteroskedastic linear regression model. The test compares the conventional F-statistic to a critical value that corrects for many restrictions and conditional heteroskedasticity. The correction utilizes leave-one-out estimation to recenter the conventional critical value and leave-three-out estimation to rescale it. Large sample properties of the test are established in an asymptotic framework where the number of tested restrictions may grow in proportion to the number of observations. We show that the test is asymptotically valid and has non-trivial asymptotic power against the same local alternatives as the exact F test when the latter is valid. Simulations corroborate the relevance of these theoretical findings and suggest excellent size control in moderately small samples also under strong heteroskedasticity.
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