dcor.ttest: Distance Correlation t-Test

Description Usage Arguments Details Value Author(s) References See Also Examples

View source: R/dcorT.R

Description

Distance correlation t-test of multivariate independence.

Usage

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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

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.

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, 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

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

bcdcor dcov.test dcor DCOR

Examples

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 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)

mariarizzo/energy documentation built on Oct. 30, 2018, 3:15 p.m.