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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 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.

See also

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• Correlation
• Kendall's tau
• Spearman's rank correlation coefficient
• Distance correlation

Notes

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Primary sources

• 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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