The Annals of Statistics
- Ann. Statist.
- Volume 13, Number 3 (1985), 1140-1155.
Sobolev Tests for Independence of Directions
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
