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
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.
