# 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

$H=\int (F_{{12}}-F_{1}F_{2})^{2}\,dF_{{12}}\!$

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[1] 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.