Hoeffding's independence test

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 {\displaystyle H=\int (F_{12}-F_{1}F_{2})^{2}\,dF_{12}} where F 12 {\displaystyle F_{12}} is the joint distribution function of two random variables, and F 1 {\displaystyle F_{1}} and F 2 {\displaystyle F_{2}} are their marginal distribution functions. Hoeffding derived an unbiased estimator of H {\displaystyle H} that can be used to test for independence, and is consistent for any continuous alternative.

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