- JYX front page
- →
- Articles
- →
- Faculty of Mathematics and Science
- →
- View Item

JavaScript is disabled for your browser. Some features of this site may not work without it.

Citation:

Taskinen, S., Randles, R., & Oja, H. (2005). Multivariate nonparametric tests of independence. *Journal of the American Statistical Association*, 100 (471), 916-925. doi:10.1198/016214505000000097

Title: | Multivariate nonparametric tests of independence |

Author: | Taskinen, Sara; Randles, Ronald; Oja, Hannu |

Abstract: | New test statistics are proposed for testing whether two random vectors are independent. Gieser and Randles, as well as Taskinen, Kankainen, and Oja have introduced and discussed multivariate extensions of the quadrant test of Blomqvist. This article serves as a sequel to this work and presents new multivariate extensions of Kendall's tau and Spearman's rho statistics. Two different approaches are discussed. First, interdirection proportions are used to estimate the cosines of angles between centered observation vectors and between differences of observation vectors. Second, covariances between affine-equivariant multivariate signs and ranks are used. The test statistics arising from these two approaches appear to be asymptotically equivalent if each vector is elliptically symmetric. The spatial sign versions are easy to compute for data in common dimensions, and they provide practical, robust alternatives to normal-theory methods. Asymptotic theory is developed to approximate the finite-sample null distributions as well, as to calculate limiting Pitman efficiencies. Small-sample null permutation distributions are also described. A simple simulation study is used to compare the proposed tests with the classical Wilks test. Finally, the theory is illustrated by an example. ... |

Publisher: | American Statistical Association |

Date: | 2005 |

Belongs to series: | Journal of the American Statistical Association |

ISSN: | 0162-1459 |

Subjects: | riippumattomuus affine invariance Kendall's tau Pitman efficiency Quadrant test Robustness Spearman's rho |

Rights: | © American Statistical Association. This is an author's final draft version of an article whose final and definitive form has been published by American Statistical Association. |

DOI: | 10.1198/016214505000000097 |

Permanent link to this item: http://urn.fi/URN:NBN:fi:jyu-201211293122

- Sign test of independence between two random vectors (2003)
- Tests of multinormality based on location vectors and scatter matrices (2007)
- Robustifying principal component analysis with spatial sign vectors (2012)
- Sign and rank covariance matrices with applications to multivariate analysis (2002)
- k-Step shape estimators based on spatial signs and ranks (2010)

- Independent component analysis based on symmetrised scatter matrices (2007)
- Sign test of independence between two random vectors (2003)
- On Mardia's tests of multinormality (2004)
- Robustifying principal component analysis with spatial sign vectors (2012)
- Rank scores tests of multivariate independence (2004)
- Affine-invariant rank tests for multivariate independence in independent component models (2016)
- k-Step shape estimators based on spatial signs and ranks (2010)
- Tests of multinormality based on location vectors and scatter matrices (2007)
- Deflation-based separation of uncorrelated stationary time series (2014)
- Influence functions and efficiencies of the canonical correlation and vector estimates based on scatter and shape matrices (2006)