energy (version 1.6.2)

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) bcdcor(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, bcdcor returns the bias corrected dcor 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. dcor.t returns the t statistic and bcdcor returns the bias corrected distance correlation statistic. 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

dcov.test dcor DCOR

Examples

Run this code
 x <- matrix(rnorm(100), 10, 10)
 y <- matrix(runif(100), 10, 10)
 dx <- dist(x)
 dy <- dist(y)
 dcor.t(x, y)
 bcdcor(dx, dy, distance=TRUE)
 dcor.ttest(x, y)

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