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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
 
:<math>H = \int (F_{12}-F_1F_2)^2 \, dF_{12} \!</math>
 
where <math>F_{12}</math> is the [[joint distribution function]] of two random variables, and <math>F_1</math> and <math>F_2</math> are their [[marginal distribution]] functions.
Hoeffding derived an [[unbiased estimator]] of <math>H</math> that can be used to test for [[independence (probability theory)|independence]], and is [[consistent estimator|consistent]] for any continuous [[alternative hypothesis|alternative]]. The test should only be applied to data drawn from a [[continuous probability distribution|continuous distribution]], since <math>H</math> has a defect for discontinuous <math>F_{12}</math>, namely that it is not necessarily zero when <math>F_{12}=F_1F_2</math>.
 
A recent paper<ref>Wilding, G.E., Mudholkar, G.S. (2008) [http://www.sciencedirect.com/science/article/B7CRS-4PJ04Y7-1/2/e10c0f978e665a0d5ffd41a594f9a9ba "Empirical approximations for Hoeffding's test of bivariate independence using two Weibull extensions"], ''Statistical Methodology'', 5 (2), 160-&ndash;170</ref> 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==
 
{{Portal|Statistics}}
* [[Correlation]]
* [[Kendall's tau]]
* [[Spearman's rank correlation coefficient]]
*[[Distance correlation]]
 
==Notes==
{{Reflist}}
 
==Primary sources==
* Wassily Hoeffding, A non-parametric test of independence, ''Annals of Mathematical Statistics'' '''19''': 293&ndash;325, 1948. ([http://www.jstor.org/stable/2236021 JSTOR])
* Hollander and Wolfe, Non-parametric statistical methods (Section 8.7), 1999. Wiley.
 
{{DEFAULTSORT:Hoeffding's Independence Test}}
[[Category:Covariance and correlation]]
[[Category:Non-parametric statistics]]
[[Category:Statistical tests]]
[[Category:Statistical dependence]]
 
 
{{statistics-stub}}

Revision as of 00:48, 29 November 2013

In statistics, Hoeffding's test of independence, named after Wassily Hoeffding, is a test based on the population measure of deviation from independence

where is the joint distribution function of two random variables, and and are their marginal distribution functions. Hoeffding derived an unbiased estimator of 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 has a defect for discontinuous , namely that it is not necessarily zero when .

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

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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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  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
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