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BUILT-IN MATHEMATICA SYMBOL
HoeffdingD
HoeffdingD[v1, v2]
gives Hoeffding's dependence measure 
for the vectors 
and 
.
HoeffdingD[m]
gives Hoeffding's dependence measure for the matrix m.
HoeffdingD[m1, m2]
gives Hoeffding's dependence measure for the matrices 
and 
.
HoeffdingD[dist]
gives Hoeffding's matrix for the multivariate symbolic distribution dist.
HoeffdingD[dist, i, j]
gives the 
element of for the multivariate symbolic distribution dist.
Details
- HoeffdingD[v1, v2] gives Hoeffding's dependence measure
between 
and 
. - Hoeffding's is a measure of dependence based on the relative order of elements in the two lists.
- Hoeffding's between
and 
is given by ![30 (-2 (n-2) R+(n-3) (n-2) S+Q)/TemplateBox[{{n, -, 4}, 5}, Pochhammer]](Files/HoeffdingD.en/13.png "30 (-2 (n-2) R+(n-3) (n-2) S+Q)/TemplateBox[{{n, -, 4}, 5}, Pochhammer]")
, where 
is the number of observations in 
, 
, 
, 
, 
for 
, 
is the rank of 
, 
is the rank of 
and 
is equal to Boole[a<b]. - The arguments
and 
can be any real-valued vectors of equal length greater than 5. - For a matrix m with
columns, HoeffdingD[m] is a 
×
matrix of the dependence measures between columns of m. - For an
×
matrix 
and an 
×
matrix 
, HoeffdingD[m1, m2] is a 
×
matrix of the dependence measures between columns of 
and columns of 
. - HoeffdingD[dist, i, j] is given by 30 Expectation[(F[x, y]-G[x]H[y])^2, {x, y}
disti, j] where 
, 
, and 
are the the CDFs of the 
, 
, and 
marginals of dist respectively. - HoeffdingD[dist] gives a matrix where the
entry is given by HoeffdingD[dist, i, j].
New in 9
