The Annals of Statistics

Sobolev Tests for Independence of Directions

P. E. Jupp and B. D. Spurr

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Abstract

Two families of invariant tests for independence of random variables on compact Riemannian manifolds are proposed and studied. The tests are based on Gine's Sobolev norms which are obtained by mapping the manifolds into Hilbert spaces. For general compact manifolds, randomization tests are suggested. For the bivariate circular case, distribution-free tests based on uniform scores are considered.

Article information

Source
Ann. Statist., Volume 13, Number 3 (1985), 1140-1155.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176349661

Digital Object Identifier
doi:10.1214/aos/1176349661

Mathematical Reviews number (MathSciNet)
MR803763

Zentralblatt MATH identifier
0585.62098

JSTOR
links.jstor.org

Subjects
Primary: 62H15: Hypothesis testing
Secondary: 62H20: Measures of association (correlation, canonical correlation, etc.) 62G10: Hypothesis testing 62E20: Asymptotic distribution theory

Keywords
Consistency correlation directional data independence invariance randomization tests Riemannian manifolds uniform scores

Citation

Jupp, P. E.; Spurr, B. D. Sobolev Tests for Independence of Directions. Ann. Statist. 13 (1985), no. 3, 1140--1155. doi:10.1214/aos/1176349661. https://projecteuclid.org/euclid.aos/1176349661


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