No abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Biometrika Trust is collaborating with JSTOR to digitize, preserve and extend access to Biometrika. SUMMARY A new invariant test for uniformity on the circle is presented. The motivation of this paper was to find a test consistent against all possible alternatives that would be powerful against both unimodal and bimodal alternatives. An index of performance is used to obtain the kernel of our statistic in the class of Sobolev statistics defined by Gine (1975). The power of the test against Stephens's (1969) alternatives is investigated by simulation including comparisons with the An test of Ajne and the Un2 test of Watson which are two classical Sobolev statistics.Some key words: Ajne's test; Directional data; Sobolev statistic on the circle; Stephens's alternatives; Test of uniformity; U-statistic; Watson's test.