Hoeffding's independence test
where is the joint distribution function of two random variables, and and are their marginal distribution functions. Hoeffding derived an unbiased estimator of that can be used to test for independence, and is consistent for any continuous alternative. The test should only be applied to data drawn from a continuous distribution, since has a defect for discontinuous , namely that it is not necessarily zero when .
A recent paper describes both the calculation of a sample based version of this measure for use as a test statistic, and calculation of the null distribution of this test statistic.
- Wilding, G.E., Mudholkar, G.S. (2008) "Empirical approximations for Hoeffding's test of bivariate independence using two Weibull extensions", Statistical Methodology, 5 (2), 160-–170
- Wassily Hoeffding, A non-parametric test of independence, Annals of Mathematical Statistics 19: 293–325, 1948. (JSTOR)
- Hollander and Wolfe, Non-parametric statistical methods (Section 8.7), 1999. Wiley.
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