Description Usage Arguments Details Value Note Author(s) References Examples

Stand-alone double centering and U-centering functions that are applied in unbiased distance covariance, bias corrected distance correlation, and partial distance correlation.

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`x` |
dist object or data matrix |

`Dx` |
distance or dissimilarity matrix |

In `Dcenter`

and `Ucenter`

, `x`

must be
a `dist`

object or a data matrix. Both functions return
a doubly centered distance matrix.

Note that `pdcor`

, etc. functions include the
centering operations (in C), so that these stand alone versions
of centering functions are not needed except in case one
wants to compute just a double-centered or U-centered matrix.

`U_center`

is the Rcpp export of the cpp function.
`D_center`

is the Rcpp export of the cpp function.

All functions return a square symmetric matrix.

`Dcenter`

returns a matrix

*A_{ij}=a_{ij} - \bar a_{i.} - \bar a_{.j} + \bar a_{..}*

as in classical multidimensional scaling. `Ucenter`

returns a matrix

*\tilde A_{ij}=a_{ij} - \frac{a_{i.}}{n-2}
- \frac{a_{.j}}{n-2} + \frac{a_{..}}{(n-1)(n-2)},\quad i \neq j,*

with zero diagonal,
and this is the double centering applied in `pdcov`

and
`pdcor`

as well as the unbiased dCov and bias corrected
dCor statistics.

The c++ versions `D_center`

and `U_center`

should typically
be faster. R versions are retained for historical reasons.

Maria L. Rizzo mrizzo @ bgsu.edu and Gabor J. Szekely

Szekely, G.J. and Rizzo, M.L. (2014),
Partial Distance Correlation with Methods for Dissimilarities,
*Annals of Statistics*, Vol. 42, No. 6, pp. 2382-2412.

https://projecteuclid.org/euclid.aos/1413810731

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