indep.etest {energy}R Documentation

Energy Statistic Test of Independence

Description

Deprecated: use indep.test with method = mvI. Computes a multivariate nonparametric E-statistic and test of independence.

Usage

indep.e(x, y)
indep.etest(x, y, R=199)

Arguments

x matrix: first sample, observations in rows
y matrix: second sample, observations in rows
R number of replicates

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.

Value

The sample coefficient I is returned by indep.e. The function indep.etest returns a list with class htest containing

method description of test
statistic observed value of the coefficient I
p.value approximate p-value of the test
data.name description of data

Author(s)

Maria L. Rizzo mrizzo @ bgnet.bgsu.edu and Gabor J. Szekely gabors @ bgnet.bgsu.edu

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

Examples

 ## Not run: 
 ## independent univariate data
 x <- sin(runif(30, 0, 2*pi) * 2)
 y <- sin(runif(30, 0, 2*pi) * 4)
 indep.etest(x, y, R = 99)

 ## dependent univariate data
 u <- runif(30, 0, 2*pi)
 x <- sin(2 * u)
 y <- sin(3 * u)
 indep.etest(x, y, R = 99)
 
 u <- runif(50, 0, 2*pi)
 x <- sin(2 * u)
 y <- sin(4 * u)
 indep.etest(x, y, R = 99)
 
 ## independent multivariate data
 x <- matrix(rnorm(60), nrow=20, ncol=3)
 y <- matrix(rnorm(40), nrow=20, ncol=2)
 indep.e(x, y)
 indep.etest(x, y, R = 99)
 
 ## independent bivariate data
 x <- matrix(rnorm(50), nrow=25, ncol=2)
 y <- matrix(rnorm(50), nrow=25, ncol=2)
 indep.e(x, y)
 indep.etest(x, y, R = 99)
 
 ## dependent bivariate data
 library(MASS)
 Sigma <- matrix(c(1, .5, .5, 1), 2, 2)
 x <- mvrnorm(30, c(0, 0), Sigma)
 indep.etest(x[,1], x[,2], R = 99)
 
 ## dependent multivariate data
 Sigma <- matrix(c(1, .1, 0, 0 , 1, 0, 0 ,.1, 1), 3, 3)
 x <- mvrnorm(30, c(0, 0, 0), diag(3))
 y <- mvrnorm(30, c(0, 0, 0), Sigma) * x
 indep.etest(x, y, R = 99)
 ## End(Not run)

[Package energy version 1.1-0 Index]