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.

## DetailsDetails

• 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 , 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].

## ExamplesExamplesopen allclose all

### Basic Examples (4)Basic Examples (4)

Hoeffding's for two vectors:

 Out[2]=

Hoeffding's for a matrix:

 Out[2]//MatrixForm=

Hoeffding's for two matrices:

 Out[3]//MatrixForm=

Compute Hoeffding's for a bivariate distribution:

 Out[2]//MatrixForm=

Compare to a simulated value:

 Out[3]//MatrixForm=