Implicit Alternatives and the Local Power of Test Statistics
AbstractThe local power of test statistics is analyzed by considering sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative. The three classical test statistics-LR, Wald, and LM-are shown to tend asymptot ically to the same random variable under all such sequences. The powe r of these statistics depends on the null, the alternative, and the sequence of DGPs in a geometrically intuitive way. This implies that, for any statistic that is asymptotically chi-squared under the null, there exists an "implicit alternative hypothesis" against which that statistic will have highest power. Copyright 1987 by The Econometric Society.
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Bibliographic InfoArticle provided by Econometric Society in its journal Econometrica.
Volume (Year): 55 (1987)
Issue (Month): 6 (November)
Other versions of this item:
- Davidson , R. & Mackinnon, J.G., 1985. "Implicit alternatives and the local power of test statistics," CORE Discussion Papers 1985025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Russell Davidson & James G. MacKinnon, 1984. "Implicit Alternatives and the Local Power of Test Statistics," Working Papers 556, Queen's University, Department of Economics.
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