Hoeffding's independence test

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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_1F_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_1F_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.

See also[edit]


  1. ^ Wilding, G.E., Mudholkar, G.S. (2008) "Empirical approximations for Hoeffding's test of bivariate independence using two Weibull extensions", Statistical Methodology, 5 (2), 160-–170

Primary sources[edit]

  • 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.