论文信息 - U-statistics based on the Green's function of the Laplacian on the circle and the sphere - 字舞流文

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

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.

J.-R. Pycke | J. Pycke

[1] I. Chavel. Eigenvalues in Riemannian geometry , 1984 .

[2] S. Yau. Mathematics and its applications , 2002 .

[3] J. Durbin. Distribution theory for tests based on the sample distribution function , 1973 .

[4] N. Bingham. EMPIRICAL PROCESSES WITH APPLICATIONS TO STATISTICS (Wiley Series in Probability and Mathematical Statistics) , 1987 .

[5] J. Pycke. Multivariate extensions of the Anderson-Darling process , 2003 .

[6] G. S. Watson,et al. Goodness-of-fit tests on a circle. II , 1961 .

[7] P. Janssen,et al. Theory of U-statistics , 1994 .

[8] P. Deheuvels,et al. Karhunen-Loève Expansions for Weighted Wiener Processes and Brownian Bridges via Bessel Functions , 2003 .

[9] Harry Dym,et al. Fourier series and integrals , 1972 .

[10] Kehe Zhu. Operator theory in function spaces , 1990 .

[11] James Durbin,et al. Components of Cramer-von Mises statistics. I , 1972 .

[12] J. Wellner,et al. Empirical Processes with Applications to Statistics , 2009 .

[13] Thierry Aubin,et al. Nonlinear analysis on manifolds, Monge-Ampère equations , 1982 .

[14] M. Giné,et al. Invariant Tests for Uniformity on Compact Riemannian Manifolds Based on Sobolev Norms , 1975 .

[15] G. Tolstov. Fourier Series , 1962 .