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Implicit Alternatives and the Local Power of Test Statistics

  • Davidson, Russell
  • MacKinnon, James G

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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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 55 (1987)
Issue (Month): 6 (November)
Pages: 1305-29

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Handle: RePEc:ecm:emetrp:v:55:y:1987:i:6:p:1305-29
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