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Implicit alternatives and the local power of test statistics

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  • DAVIDSON , R.
  • MACKINNON, J.G.

Abstract

The 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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Suggested Citation

  • Davidson , R. & Mackinnon, J.G., 1985. "Implicit alternatives and the local power of test statistics," LIDAM Discussion Papers CORE 1985025, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvco:1985025
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