Get access

Comparison of Maximum Statistics for Hypothesis Testing When a Nuisance Parameter Is Present only under the Alternative


  • Gang Zheng,

    1. Office of Biostatistics Research, DECA, National Heart, Lung and Blood Institute, 6701 Rockledge Drive, MSC 7938, Bethesda, Maryland 20892, U.S.A.
    Search for more papers by this author
  • Zehua Chen

    1. Department of Statistics and Applied Probability, National University of Singapore, 10 Kent Ridge Crescent, Singapore 119260, Republic of Singapore
    Search for more papers by this author



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.

Get access to the full text of this article