R: Unbiased dcov and bias-corrected dcor statistics

Unbiased distance covariance {energy} | R Documentation

## 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)

### Arguments

`x` | data or dist object of first sample
`y` | data or dist object of second sample

### 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.

### Value

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

### Note

Unbiased distance covariance (SR2014) corresponds to the biased (original) dCov^2. Since `dcovU` is an unbiased statistic, it is signed and we do not take the square root. For the original distance covariance test of independence (SRB2007, SR2009), the distance covariance test statistic is the V-statistic n V_n^2 (not dCov). Similarly, `bcdcor` is bias-corrected, so we do not take the square root as with dCor.

### Author(s)

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

### 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

     x <- iris[1:50, 1:4]
     y <- iris[51:100, 1:4]
     dcovU(x, y)
     bcdcor(x, y)

[Package energy version 1.7-6 Index]