Comparison of Maximum Statistics for Hypothesis Testing When a Nuisance Parameter Is Present only under the Alternative
Article first published online: 28 FEB 2005
Volume 61, Issue 1, pages 254–258, March 2005
How to Cite
Zheng, G. and Chen, Z. (2005), Comparison of Maximum Statistics for Hypothesis Testing When a Nuisance Parameter Is Present only under the Alternative. Biometrics, 61: 254–258. doi: 10.1111/j.0006-341X.2005.030531.x
- Issue published online: 28 FEB 2005
- Article first published online: 28 FEB 2005
- Received May 2003. Revised April 2004. Accepted May 2004.
- Genetic analysis;
- Maximum statistics;
- Score test
Summary In many practical problems, a hypothesis testing involves a nuisance parameter which appears only under the alternative hypothesis. Davies (1977, Biometrika64, 247–254) proposed the maximum of the score statistics over the whole range of the nuisance parameter as a test statistic for this type of hypothesis testing. Freidlin, Podgor, and Gastwirth (1999, Biometrics55, 883–886) studied two other simpler maximum test statistics, the maximum of the score statistics at two extreme points of the nuisance parameter, and the maximum of the score statistics at three points of the nuisance parameter including the two extreme points. In this article, we compare the powers of these three maximum-type statistics in the context of three genetic problems.