Likelihood ratio tests with boundary constraints using data-dependent degrees of freedom

• 成果类型: Article
• 署名作者: Susko, Edward
• 署名单位: Dalhousie University
• 刊物名称: BIOMETRIKA
• ISSN/ISSBN: 0006-3444
• DOI: 10.1093/biomet/ast032
• 发表日期: 2013
• 页码: 10191023
• 关键词: asymptotic-distribution; nonstandard conditions; composite hypotheses; variance-components

摘要

When the null hypothesis constrains parameters to the boundary of the parameter space, the asymptotic null distribution of the likelihood ratio statistic is often a mixture of chi-squared distributions, giving rise to the so-called chi-bar test, where weights can depend on the true unknown parameter and be difficult to calculate. We consider the test that conditions on the observed number of null hypothesis parameters in the interior of the parameter space. This approach uses simple chi-squared thresholds, yields conservative asymptotic Type I error, and is guaranteed to give power improvements over the naive approach of simply ignoring boundary constraints. Simulations validate the theoretical results, illustrate application settings, and find power comparable with but usually less than that of the chi-bar test.