energy (version 1.7-12)

dcovU_stats: Unbiased distance covariance statistics

Description

This function computes unbiased estimators of squared distance covariance, distance variance, and a bias-corrected estimator of (squared) distance correlation.

Usage

dcovU_stats(Dx, Dy)

Value

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

Arguments

Dx

distance matrix of first sample

Dy

distance matrix of second sample

Author

Maria L. Rizzo and Gabor J. Szekely

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. The arguments must be square symmetric matrices.

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.
tools:::Rd_expr_doi("10.1214/009053607000000505")

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

Examples

 x <- iris[1:50, 1:4]
 y <- iris[51:100, 1:4]
 Dx <- as.matrix(dist(x))
 Dy <- as.matrix(dist(y))
 dcovU_stats(Dx, Dy)