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A nonparametric test for independence based on sample space partitions

Olivier Thas (UGent) and Jean-Pierre Ottoy (UGent)
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Abstract
In this paper, a class of nonparametric tests for independence between two continuous random variables is proposed. The members of the class are characterized by the size of the partitions of the sample space on which the test statistics are based. The test statistic that corresponds to the smallest partition size may be seen as an extension of Hoeffding's statistic with an Anderson-Darling-type weight function. In this simplest case, we have proven its asymptotic null distribution as well as its omnibus consistency. In a simulation study, the powers of the new tests are compared to those of some other tests for independence. It is concluded that overall high powers are obtained with these new tests.
Keywords
rank statistic, nonparametric test, power, statistical independence

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Please use this url to cite or link to this publication:

MLA
Thas, Olivier, and Jean-Pierre Ottoy. “A Nonparametric Test for Independence Based on Sample Space Partitions.” COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION 33.3 (2004): 711–728. Print.
APA
Thas, O., & Ottoy, J.-P. (2004). A nonparametric test for independence based on sample space partitions. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, 33(3), 711–728.
Chicago author-date
Thas, Olivier, and Jean-Pierre Ottoy. 2004. “A Nonparametric Test for Independence Based on Sample Space Partitions.” Communications in Statistics-simulation and Computation 33 (3): 711–728.
Chicago author-date (all authors)
Thas, Olivier, and Jean-Pierre Ottoy. 2004. “A Nonparametric Test for Independence Based on Sample Space Partitions.” Communications in Statistics-simulation and Computation 33 (3): 711–728.
Vancouver
1.
Thas O, Ottoy J-P. A nonparametric test for independence based on sample space partitions. COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION. 2004;33(3):711–28.
IEEE
[1]
O. Thas and J.-P. Ottoy, “A nonparametric test for independence based on sample space partitions,” COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION, vol. 33, no. 3, pp. 711–728, 2004.
@article{338426,
  abstract     = {In this paper, a class of nonparametric tests for independence between two continuous random variables is proposed. The members of the class are characterized by the size of the partitions of the sample space on which the test statistics are based. The test statistic that corresponds to the smallest partition size may be seen as an extension of Hoeffding's statistic with an Anderson-Darling-type weight function. In this simplest case, we have proven its asymptotic null distribution as well as its omnibus consistency. In a simulation study, the powers of the new tests are compared to those of some other tests for independence. It is concluded that overall high powers are obtained with these new tests.},
  author       = {Thas, Olivier and Ottoy, Jean-Pierre},
  issn         = {0361-0918},
  journal      = {COMMUNICATIONS IN STATISTICS-SIMULATION AND COMPUTATION},
  keywords     = {rank statistic,nonparametric test,power,statistical independence},
  language     = {eng},
  number       = {3},
  pages        = {711--728},
  title        = {A nonparametric test for independence based on sample space partitions},
  url          = {http://dx.doi.org/10.1081/SAC-200033335},
  volume       = {33},
  year         = {2004},
}

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