energy (version 1.7-2)

dcor.ttest: 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

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

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 \(n \geq 10\) 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. 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.

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

# NOT RUN {
 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)
# }