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 ^(th) 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 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}Distributeddisti, j] where , , and are the the CDFs of the ^(th), ^(th), and ^(th) marginals of dist respectively.
  • HoeffdingD[dist] gives a matrix where the ^(th) entry is given by HoeffdingD[dist, i, j].

ExamplesExamplesopen allclose all

Basic Examples (4)Basic Examples (4)

Hoeffding's for two vectors:

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Hoeffding's for a matrix:

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Hoeffding's for two matrices:

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Compute Hoeffding's for a bivariate distribution:

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Compare to a simulated value:

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