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An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes

Olivier Thas (UGent) and Jean-Pierre Ottoy (UGent)
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Abstract
In this paper we first show that the k -sample Anderson-Darling test is basically an average of Pearson statistics in 2 x k contingency tables that are induced by observation-based partitions of the sample space. As an extension, we construct a family of rank test statistics, indexed by c is an element of N, which is based on similarly constructed c x k partitions. An extensive simulation study, in which we compare the new test with others, suggests that generally very high powers are obtained with the new tests. Finally we propose a decomposition of the test statistic in interpretable components.
Keywords
power, distribution-free test, rank statistic, SQUARED DISTANCE MEASURE, GOODNESS-OF-FIT, STATISTICS, COMPONENTS

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MLA
Thas, Olivier, and Jean-Pierre Ottoy. “An Extension of the Anderson-Darling K-sample Test to Arbitrary Sample Space Partition Sizes.” JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION 74.9 (2004): 651–665. Print.
APA
Thas, O., & Ottoy, J.-P. (2004). An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 74(9), 651–665.
Chicago author-date
Thas, Olivier, and Jean-Pierre Ottoy. 2004. “An Extension of the Anderson-Darling K-sample Test to Arbitrary Sample Space Partition Sizes.” Journal of Statistical Computation and Simulation 74 (9): 651–665.
Chicago author-date (all authors)
Thas, Olivier, and Jean-Pierre Ottoy. 2004. “An Extension of the Anderson-Darling K-sample Test to Arbitrary Sample Space Partition Sizes.” Journal of Statistical Computation and Simulation 74 (9): 651–665.
Vancouver
1.
Thas O, Ottoy J-P. An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION. 2004;74(9):651–65.
IEEE
[1]
O. Thas and J.-P. Ottoy, “An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes,” JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, vol. 74, no. 9, pp. 651–665, 2004.
@article{338436,
  abstract     = {In this paper we first show that the k -sample Anderson-Darling test is basically an average of Pearson statistics in 2 x k contingency tables that are induced by observation-based partitions of the sample space. As an extension, we construct a family of rank test statistics, indexed by c is an element of N, which is based on similarly constructed c x k partitions. An extensive simulation study, in which we compare the new test with others, suggests that generally very high powers are obtained with the new tests. Finally we propose a decomposition of the test statistic in interpretable components.},
  author       = {Thas, Olivier and Ottoy, Jean-Pierre},
  issn         = {0094-9655},
  journal      = {JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION},
  keywords     = {power,distribution-free test,rank statistic,SQUARED DISTANCE MEASURE,GOODNESS-OF-FIT,STATISTICS,COMPONENTS},
  language     = {eng},
  number       = {9},
  pages        = {651--665},
  title        = {An extension of the Anderson-Darling k-sample test to arbitrary sample space partition sizes},
  url          = {http://dx.doi.org/10.1080/00949650310001623399},
  volume       = {74},
  year         = {2004},
}

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