energy (version 1.7-11)

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

Description

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

Usage

bcdcor(x, y)
dcovU(x, y)

Value

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

Arguments

x

data or dist object of first sample

y

data or dist object 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.

Argument types supported are numeric data matrix, data.frame, or tibble, with observations in rows; numeric vector; ordered or unordered factors. In case of unordered factors a 0-1 distance matrix is computed.

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]
 dcovU(x, y)
 bcdcor(x, y)