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. The test should only be applied to data drawn from a continuous distribution, since H {\displaystyle H} has a defect for discontinuous F 12 {\displaystyle F_{12}} , namely that it is not necessarily zero when F 12 = F 1 F 2 {\displaystyle F_{12}=F_{1}F_{2}} . This drawback can be overcome by taking an integration with respect to d F 1 F 2 {\displaystyle dF_{1}F_{2}} . 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.
See also
Correlation Kendall's tau Spearman's rank correlation coefficient Distance correlation
References
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.