A New Sobolev Test for Uniformity on the Circle
提出一种新的圆上均匀性检验，对单峰和双峰备择假设都有较高功效，通过模拟与经典Sobolev统计量比较，验证了其性能。
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 Giné (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.