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

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.

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.

Value

dcor.t returns the t statistic, bcdcor returns the bias corrected dcor statistic, and dcor.ttest returns a list with class htest containing

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

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)
 bcdcor(dx, dy, distance=TRUE)
 dcor.ttest(x, y)

Results