Econometrica Vol. 55 No. 6 1987
Implicit Alternatives and the Local Power of Test Statistics
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.
- DOI
- 10.2307/1913558
- Volume
- 55
- Issue
- 6
- Pages
- 1305
- Sources
- bibtex:phds-export.bib crossref openalex