A note on a family of criteria for evaluating test statistics. Issue 11 (2nd June 2016)

• Record Type: Journal Article
• Authors: Anderson, Gordon; Leo, Teng Wah
• Is Part Of: Communications in statistics. Volume 45:Issue 11(2016)
• Page Start: 3138
• Page End: 3144
• Publication Date: 2016-06-02
• Subjects: Mathematical statistics -- Periodicals; Mathematics; Statistics; 519.2
• DOI: 10.1080/03610926.2014.897137
• Languages: English
• ISSNs: 0361-0926

Abstract

ABSTRACT: In noting that the usual criteria for choosing an optimal test, Uniform Power and Local Power are at opposite ends of a spectrum of dominance criteria, a complete "Power Dominance" family of criteria for classifying and choosing optimal tests on the basis of their power characteristics is identified, wherein successive orders of dominance attach increasing weight to power close to the null hypothesis. Indices of the extent to which a preferred test has superior power characteristics over other members in its class, and an index of the proximity of a test to the envelope function of alternative tests are also provided. The ideas are exemplified using various optimal test statistics for Normal and Laplace population distributions.