Statistical measure
In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence
formula_1
where formula_2 is the joint distribution function of two random variables, and formula_3 and formula_4 are their marginal distribution functions.
Hoeffding derived an unbiased estimator of formula_5 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 formula_5 has a defect for discontinuous formula_2, namely that it is not necessarily zero when formula_8. This drawback can be overcome by taking an integration with respect to formula_9. This modified measure is known as Blum–Kiefer–Rosenblatt coefficient.
A paper published in 2008 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.
References.
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