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A comparison of nonparametric tests of independence

University of British Columbia

The nonparametrie tests of bivariate independence, based on Spearman's rho, Kendall's tau, the Blum-Kiefer-Rosenblatt statistic, the Fisher-Yates normal scores coefficient and the quadrant sum are compared with the parametric test based on the ordinary correlation coefficient. The tests are compared in the bivariate normal case by recording the Pitman and Bahadur efficiencies of each test. The empirical powers resulting from a Monte Carlo study are also given for the tests. The components of the Blum-Kiefer-Rosenblatt statistic are derived and are related to linear rank statistics. The rank statistic associated with the first component is suggested as a new nonparametric test of independence. This test is included in the comparison and is shown to perform reasonably well. As one sided tests of independence in bivariate populations the Fisher-Yates coefficient and the sample correlation coefficient are to be preferred over the other tests. As two sided tests the Blum-Kiefer-Rosenblatt statistic is the best test for alternatives near the null hypothesis. When the alternatives are distant from the null hypothesis the Fisher-Yates coefficient or the sample correlation coefficient should be used. The quadrant sum always performs poorly while the other nonparametric tests, including that based on the first component of the Blum-Kiefer-Rosenblatt statistic are acceptable tests.

Text

2010-02-24

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http://hdl.handle.net/2429/20875

Mathematics

University of British Columbia

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