Abstract
We define a test statistic C n based on the sum of the likelihood ratio statistics for testing independence in the 2 × 2 tables defined at n sample cut-points (X i , Y i ). The asymptotic distribution of C n , given the cut-points, is sum of dependent χ2 variables with one degree of freedom. We use the bootstrap to obtain the distribution of C n . We compare the performance of several tests of bivariate independence, including Pearson, Spearman, and Kendall correlations, Blum-Kiefer-Rosenblatt statistic, and C n under several copulas and given marginal distributions.
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