Distance correlation t-test of multivariate independence for high dimension.
dcorT.test(x, y)
dcorT(x, y)dcorT returns the dcor t statistic, and
dcorT.test returns a list with class htest containing
description of test
observed value of the test statistic
degrees of freedom
(bias corrected) squared dCor(x,y)
p-value of the t-test
description of data
data or distances of first sample
data or distances of second sample
Maria L. Rizzo mrizzo@bgsu.edu and Gabor J. Szekely
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.
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.
tools:::Rd_expr_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.
tools:::Rd_expr_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.
tools:::Rd_expr_doi("10.1214/09-AOAS312")
bcdcor dcov.test dcor DCOR
x <- matrix(rnorm(100), 10, 10)
y <- matrix(runif(100), 10, 10)
dcorT(x, y)
dcorT.test(x, y)
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