In this paper it is shown that "classical" tests can become asymptotically inadmissible (i.e. we show that there exist uniformly better tests) if the information matrix becomes stochastic: A typical example is the augmented Dickey-Fuller test for unit roots (in case of no deterministic trend. We also apply our results to tests based on mixed-normal estimators (which typically occur in the analysis of cointegrating relationsships)
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