 On the Relationship between Directional and Omnibus Statistical TestsQian H. Li and Stephen W. Lagakos Scandinavian Journal of Statistics, 2006, vol. 33, issue 2, 239-246 Abstract: Abstract. A common statistical problem involves the testing of a K‐dimensional parameter vector. In both parametric and semiparametric settings, two types of directional tests – linear combination and constrained tests – are frequently used instead of omnibus tests in hopes of achieving greater power for specific alternatives. In this paper, we consider the relationship between these directional tests, as well as their relationship to omnibus tests. Every constrained directional test is shown to be asymptotically equivalent to a specific linear combination test under a sequence of contiguous alternatives and vice versa. Even when the direction of the alternative is known, the constrained test in general will not be optimal unless the objective function used to derive it is efficient. For an arbitrary alternative, insight into the power characteristics of directional tests in comparison to omnibus tests can be gained by a chi‐square partition of the omnibus test. Date: 2006 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:scjsta:v:33:y:2006:i:2:p:239-246 Ordering information: This journal article can be ordered from Access Statistics for this article Scandinavian Journal of Statistics is currently edited by ÿrnulf Borgan and Bo Lindqvist More articles in Scandinavian Journal of Statistics from Danish Society for Theoretical Statistics, Finnish Statistical Society, Norwegian Statistical Association, Swedish Statistical Association |
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