dcorT: Distance Correlation t-Test

In energy: E-Statistics: Multivariate Inference via the Energy of Data

Distance Correlation t-Test

Description

Distance correlation t-test of multivariate independence for high dimension.

Usage

dcorT.test(x, y)
dcorT(x, y)

Arguments

x	data or distances of first sample
y	data or distances of second sample

Details

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.

Value

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

Note

dcor.t and dcor.ttest are deprecated.

Author(s)

Maria L. Rizzo [e-mail] 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.
\Sexpr[results=rd]{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.
\Sexpr[results=rd]{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.
\Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/09-AOAS312")}

See Also

bcdcor dcov.test dcor DCOR

Examples

 x <- matrix(rnorm(100), 10, 10)
 y <- matrix(runif(100), 10, 10)
 dcorT(x, y)
 dcorT.test(x, y)

energy documentation built on Sept. 11, 2024, 7:57 p.m.