energy (version 1.7-2)

Unbiased distance covariance: Unbiased dcov and bias-corrected dcor statistics

Description

These functions compute unbiased estimators of squared distance covariance, distance variance, and a bias-corrected estimator of (squared) distance correlation.

Usage

bcdcor(x, y)
dcovU(x, y)
dcovU_stats(Dx, Dy)

Arguments

x

data or dist object of first sample

y

data or dist object of second sample

Dx

distance matrix of first sample

Dy

distance matrix of second sample

Value

dcovU returns the unbiased estimator of squared dcov. bcdcor returns a bias-corrected estimator of squared dcor.

dcovU_stats returns a vector of the components of bias-corrected dcor: [dCovU, bcdcor, dVarXU, dVarYU].

Details

The unbiased (squared) dcov is inner product definition of dCov, in the Hilbert space of U-centered distance matrices.

The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values. Arguments x, y can optionally be dist objects; otherwise these arguments are treated as data.

References

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

Szekely, G.J., Rizzo, M.L., and Bakirov, N.K. (2007), Measuring and Testing Dependence by Correlation of Distances, Annals of Statistics, Vol. 35 No. 6, pp. 2769-2794. http://dx.doi.org/10.1214/009053607000000505

Szekely, G.J. and Rizzo, M.L. (2009), Brownian Distance Covariance, Annals of Applied Statistics, Vol. 3, No. 4, 1236-1265. http://dx.doi.org/10.1214/09-AOAS312

Examples

# NOT RUN {
 x <- iris[1:50, 1:4]
 y <- iris[51:100, 1:4]
 Dx <- as.matrix(dist(x))
 Dy <- as.matrix(dist(y))

 dcovU(x, y)
 bcdcor(x, y)
 dcovU_stats(Dx, Dy)
 
# }