centering.Rd
Stand-alone double centering and U-centering functions that are applied in unbiased distance covariance, bias corrected distance correlation, and partial distance correlation.
Dcenter(x)
Ucenter(x)
U_center(Dx)
D_center(Dx)
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.
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.