A decomposition for invariant tests of uniformity on the sphere

DOI10.1090/S0002-9939-07-08804-1zbMath1112.62051MaRDI QIDQ5291946

Jean-Renaud Pycke

Publication date: 19 June 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

zbMATH Keywords

group representations\(U\)-statisticsgoodness of fit testHilbert-Schmidt operator

Mathematics Subject Classification ID

Directional data; spatial statistics (62H11) Nonparametric hypothesis testing (62G10) Ordinary representations and characters (20C15) Integral operators (47G10) Applications of operator theory in probability theory and statistics (47N30)

Related Items (9)

Computational aspects of Cui-Freeden statistics for equidistribution on the sphere ⋮ Subsampling needlet coefficients on the sphere ⋮ Recent advances in directional statistics ⋮ Group representations and high-resolution central limit theorems for subordinated spherical random fields ⋮ Some tests for uniformity of circular distributions powerful against multimodal alternatives ⋮ High-frequency asymptotics for subordinated stationary fields on an abelian compact group ⋮ Theory of generalized discrepancies on a ball of arbitrary finite dimensions and algorithms for finding low-discrepancy point sets ⋮ Representations of SO(3) and angular polyspectra ⋮ Ergodicity and Gaussianity for spherical random fields

Cites Work

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• Sobolev tests of goodness of fit of distributions on compact Riemannian manifolds
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• Large sample theory of intrinsic and extrinsic sample means on manifolds. I
• On an identity in law involving two quadratic functionals of the Brownian bridge
• Large sample theory of intrinsic and extrinsic sample means on manifolds. II.
• Approximation Theorems of Mathematical Statistics
• On an Identity in Law for the Variance of the Brownian Bridge
• Goodness-of-fit tests on a circle

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