energy (version 1.0-9)

Independence E-test: Energy Statistic Tests of Independence

Description

Computes the 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

Value

• The value of the test statistic 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 $\mathcal I$
• p.value
  approximate p-value of the test
• data.name
  description of data

concept

energy statistics

Details

Computes the coefficient $\mathcal I$ and performs a nonparametric $\mathcal E$-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 $\mathcal E = n \mathcal I^2$ 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

Examples

## 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)