Some copula-based tests of independence among several random variables having arbitrary probability distributions

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Research Article

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Over the last few decades, various copula-based methods have been proposed in the literature for testing independence among several random variables. But most of these tests are applicable only when all random variables are continuous. Only recently, a copula-based test of independence has been proposed, which also works for random variables having arbitrary probability distributions. But like most of the existing methods, this test is not invariant under monotone transformations of the variables unless the same type of transformation (either increasing or decreasing) is used for all variables. Moreover, it often yields poor results when these variables have complex non-monotone relationships. In this article, we propose some copula-based tests of independence, which take care of this problem. Our tests are invariant under strictly monotone transformations of the variables, and they can be used for continuous, discrete, or even for ordinal variables. We establish the large sample consistency of these tests under appropriate regularity conditions. Several simulated and real data sets are analysed to compare their empirical performance with some popular tests.



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