A defense of the likelihood ratio test for one-sided and order-restricted alternatives

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A defense of the likelihood ratio test for one-sided and order-restricted alternatives

TitleA defense of the likelihood ratio test for one-sided and order-restricted alternatives
Publication TypeJournal Article
Year of Publication2002
AuthorsPerlman, MD, WU, LANG
JournalJournal of Statistical Planning and Inference
Volume107
Pagination173–186
Date Publishedsep
ISSN0378-3758
AbstractIt has been asserted recently that the likelihood ratio tests (LRT) for certain multi-parameter hypothesis-testing problems with one-sided and order-restricted alternatives exhibit anomalous behaviour (Cohen and Sackrowitz (Ann. Statist. 26 (1998) 2321); Cohen et al. (J. Mult. Analysis 72 (2002) 50). For sample points x and x′ such that x′ apparently lies “deeper” inside the alternative than does x, the LRT may accept the null hypothesis for x′ but reject it for x. Like Silvapulle (Amer. Statist. 51 (1997) 178), we argue that this conclusion is not anomalous but correct for the usual formulation of the null hypothesis accompanying one-sided and order-restricted alternatives. This alleged anomaly of the LRT occurs only for an alternative hypothesis given by an obtuse convex cone C. In this case, the reformulated null hypothesis “not C” both avoids the apparent anomaly and may be more appropriate scientifically.
URLhttp://www.sciencedirect.com/science/article/pii/S0378375802002513
DOI10.1016/S0378-3758(02)00251-3