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Implicit Alternatives and the Local Power of Test Statistics Author info | Abstract | Publisher info | Download info | Related research | Statistics Russell Davidson
James G. MacKinnon
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The local power of test statistics is analyzed by extending the notion of Pitman sequences to sequences of data-generating processes (DGPs) that approach the null hypothesis without necessarily satisfying the alternative hypothesis. Under quite general conditions, the three classical test statistics -- likelihood ratio, Wald, and Lagrange multiplier -- are shown to tend asymptotically to the same random variable under all sequences of local DGPs. The power of these tests depends on the null, the alternative, and the sequence of DGPs, in a simple and geometrically intuitive way. Moreover, for any test statistic that is asymptotically Chi-squared under the null, there exists an "implicit alternative hypothesis" which coincides with the explicit alternative for the classical test statistics, and against which the test statistic will have highest power.
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Paper provided by Queen's University, Department of Economics in its series Working Papers with number
556.
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Length: 39 pages
Date of creation: 1984Date of revision:
Publication status: Published in Econometrica, 55, 1987Handle: RePEc:qed:wpaper:556Contact details of provider: Postal: Kingston, Ontario, K7L 3N6 Phone: (613) 533-2250 Fax: (613) 533-6668 Email: Web page: http://www.econ.queensu.ca/ More information through EDIRC
For technical questions regarding this item, or to correct its listing, contact: (Mark Babcock).
Keywords: power local power local alternatives Pitman sequence classical tests LM test LR test Wald test Other versions of this item:
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