U-statistics based on the Green's function of the Laplacian on the circle and the sphere

J.-R. Pycke

Statistics & Probability Letters, 2007, vol. 77, issue 9, 863-872

Abstract: We show that the Watson and Cramer-von Mises statistics are related to Green's function of the Laplacian on a circle. A generalization leads to a new U-statistic whose kernel is the Green function of the Laplacian on the sphere.

Keywords: Directional; statistics; Tests; of; uniformity; U-; and; V-statistics; Cramer-von; Mises; statistic; Anderson-Darling; statistic; Watson; statistic (search for similar items in EconPapers)
Date: 2007
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