UNIFORMLY MORE POWERFUL, ONE-SIDED TESTS FOR HYPOTHESES ABOUT LINEAR INEQUALITIES

• 成果类型: Article
• 署名作者: LIU, HM; BERGER, RL
• 署名单位: North Carolina State University
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/aos/1176324455
• 发表日期: 1995
• 页码: 55-72
• 关键词: composite

摘要

Let X have a multivariate, p-dimensional normal distribution(p greater than or equal to 2) with unknown mean mu and known, nonsingular covariance Sigma. Consider testing H-0:b(i)'mu less than or equal to 0, for some i = 1,..., k, versus H-1:b(i)'mu > 0, for all i = 1,..., k, where b(1),...,b(k), k greater than or equal to 2, are known vectors that define the hypotheses. For any 0 < alpha < 1/2, we construct a size-alpha test that is uniformly more powerful than the size-alpha likelihood ratio test (LRT). The proposed test is an intersection-union test. Other authors have presented uniformly more powerful tests under restrictions on the covariance matrix and on the hypothesis being tested. Our new test is uniformly more powerful than the LRT for all known nonsingular covariance matrices and all hypotheses. So our results show that, in a very general class of problems, the LRT can be uniformly dominated.