R: Distance Correlation t-Test

dcor.ttest {energy} | R Documentation

## Distance Correlation t-Test

### Description

Distance correlation t-test of multivariate independence.

### Usage

    dcor.ttest(x, y, distance=FALSE)
    dcor.t(x, y, distance=FALSE)

### Arguments

`x` | data or distances of first sample
`y` | data or distances of second sample
`distance` | logical: TRUE if x and y are distances

### Details

`dcor.ttest` performs a nonparametric t-test of multivariate independence in high dimension (dimension is close to or larger than sample size). The distribution of the test statistic is approximately Student t with n(n-3)/2-1 degrees of freedom and for n ≥q 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. Arguments `x`, `y` can optionally be `dist` objects or distance matrices (in this case set `distance=TRUE`).

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

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

### Value

`dcor.t` returns the t statistic, and `dcor.ttest` 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) dCor(x,y)
`p.value` | p-value of the t-test
`data.name` | description of data

### 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.
http://dx.doi.org/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.
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

### See Also

`bcdcor` `dcov.test` `dcor` `DCOR`

### Examples

     x <- matrix(rnorm(100), 10, 10)
     y <- matrix(runif(100), 10, 10)
     dx <- dist(x)
     dy <- dist(y)
     dcor.t(x, y)
     dcor.ttest(x, y)

[Package energy version 1.7-6 Index]