dcorT {energy} R Documentation

## Distance Correlation t-Test

### Description

Distance correlation t-test of multivariate independence for high dimension.

### Usage

dcorT.test(x, y)
dcorT(x, y)


### Arguments

 x data or distances of first sample y data or distances of second sample

### Details

dcorT.test performs a nonparametric t-test of multivariate independence in high dimension (dimension is close to or larger than sample size). As dimension goes to infinity, the asymptotic distribution of the test statistic is approximately Student t with n(n-3)/2-1 degrees of freedom and for n \geq 10 the statistic is approximately distributed as standard normal.

The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values.

The t statistic (dcorT) is a transformation of a bias corrected version of distance correlation (see SR 2013 for details).

Large values (upper tail) of the dcorT statistic are significant.

### Value

dcorT returns the dcor t statistic, and dcorT.test returns a list with class htest containing

  method description of test  statistic observed value of the test statistic  parameter degrees of freedom  estimate (bias corrected) squared dCor(x,y)  p.value p-value of the t-test  data.name description of data

### Note

dcor.t and dcor.ttest are deprecated.

### Author(s)

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

### References

Szekely, G.J. and Rizzo, M.L. (2013). The distance correlation t-test of independence in high dimension. Journal of Multivariate Analysis, Volume 117, pp. 193-213.
doi: 10.1016/j.jmva.2013.02.012

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.
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.
doi: 10.1214/09-AOAS312

bcdcor dcov.test dcor DCOR
 x <- matrix(rnorm(100), 10, 10)