In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence
H = ∫ ( F 12 − F 1 F 2 ) 2 d F 12 where F 12 is the joint distribution function of two random variables, and F 1 and F 2 are their marginal distribution functions. Hoeffding derived an unbiased estimator of H 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 H has a defect for discontinuous F 12 , namely that it is not necessarily zero when F 12 = F 1 F 2 .
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.
