energy (version 1.6.2)

mvI.test: Energy Statistic Test of Independence

Description

Computes the multivariate nonparametric E-statistic and test of independence based on independence coefficient $I_n$.

Usage

mvI.test(x, y, R=199) mvI(x, y)

Arguments

x

matrix: first sample, observations in rows

y

matrix: second sample, observations in rows

R

number of replicates

Value

mvI returns the statistic. mvI.test returns a list with class htest containing

method

description of test

statistic

observed value of the test statistic $n I_n^2$

estimate

$I_n$

replicates

replicates of the test statistic

p.value

approximate p-value of the test

data.name

description of data

Details

Computes the coefficient $I_n$ and performs a nonparametric $E$-test of independence. The test decision is obtained via bootstrap, with R replicates. The sample sizes (number of rows) of the two samples must agree, and samples must not contain missing values. The statistic $E = I^2$ is a ratio of V-statistics based on interpoint distances $||x_{i}-y_{j}||$. See the reference below for details.

References

Bakirov, N.K., Rizzo, M.L., and Szekely, G.J. (2006), A Multivariate Nonparametric Test of Independence, Journal of Multivariate Analysis 93/1, 58-80, http://dx.doi.org/10.1016/j.jmva.2005.10.005

See Also

indep.test mvI.test dcov.test dcov