A Test of Independence Based on the Likelihood of Cut-Points

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.

Keywords:

• Bootstrap
• Copula
• Correlation
• Dependence
• Distribution function

Mathematics Subject Classification:

• Primary 62G09, 62H17, 62H20
• Secondary 62G30, 62F03, 62F40