Implicit Alternatives and the Local Power of Test Statistics

Russell Davidson and James MacKinnon

Econometrica, 1987, vol. 55, issue 6, 1305-29

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.

Date: 1987
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Related works:
Working Paper: Implicit alternatives and the local power of test statistics (1985)
Working Paper: Implicit Alternatives and the Local Power of Test Statistics (1984)
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