Implicit Alternatives and the Local Power of Test Statistics
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.
To our knowledge, this item is not available for
download. To find whether it is available, there are three
1. Check below under "Related research" whether another version of this item is available online.
2. Check on the provider's web page whether it is in fact available.
3. Perform a search for a similarly titled item that would be available.
|Date of creation:||1984|
|Publication status:||Published in Econometrica, 55, 1987|
|Contact details of provider:|| Postal: Kingston, Ontario, K7L 3N6|
Phone: (613) 533-2250
Fax: (613) 533-6668
Web page: http://qed.econ.queensu.ca/
More information through EDIRC
When requesting a correction, please mention this item's handle: RePEc:qed:wpaper:556. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Mark Babcock)
If references are entirely missing, you can add them using this form.