Testing a model parameter when another is unidentified under the null

Abstract

Some standard test procedures, such as Score and Likelihood Ratio, replace nuisance parameters by their maximum likelihood estimates under the null hypothesis about the parameter of interest. In some models, however, a nuisance parameter is not identified under the null, so that these approaches need modification. By taking a mathematically tractable case, this paper illustrates the issues that arise and the solutions that have been proposed in the literature. The rival tests are compared in terms of power and robustness to misspecification.