eqdist.etest {energy}R Documentation

Multisample E-statistic (Energy) Test of Equal Distributions

Description

Performs the nonparametric multisample E-statistic (energy) test for equality of multivariate distributions.

Usage

 eqdist.etest(x, sizes, distance = FALSE, 
              incomplete = FALSE, N = 100, R = 999)

Arguments

x data matrix of pooled sample
sizes vector of sample sizes
distance logical: if TRUE, first argument is a distance matrix
incomplete logical: if TRUE, compute incomplete E-statistics
N incomplete sample size
R number of bootstrap replicates

Details

The k-sample multivariate E-test of equal distributions is performed. The statistic is computed from the original pooled samples, stacked in matrix x where each row is a multivariate observation, or the corresponding distance matrix. The first sizes[1] rows of x are the first sample, the next sizes[2] rows of x are the second sample, etc.

The test is implemented by nonparametric bootstrap, an approximate permutation test with R replicates.

The definition of the multisample E-statistic is given in the ksample.e documentation.

If incomplete==TRUE, incomplete E-statistics (which are incomplete V-statistics) are computed. That is, at most N observations from each sample are used, by sampling without replacement as needed.

Value

A list with class etest.eqdist containing

method Description of test
statistic Observed value of the test statistic
p.value Approximate p-value of the test
sizes Vector of sample sizes
R Number of replicates
incomplete Argument incomplete
N Argument N
replicates Vector of replicates of the statistic

Author(s)

Maria Rizzo rizzo@math.ohiou.edu

References

Szekely, G. J. and Rizzo, M. L. (2003) Testing for Equal Distributions in High Dimension, submitted.

Szekely, G. J. (2000) E-statistics: Energy of Statistical Samples, preprint.

See Also

ksample.e, print.etest.eqdist

Examples

 ## test if the 3 varieties of iris data (d=4) have equal distributions
 data(iris)
 eqdist.etest(iris[,1:4], c(50,50,50))
 
 ## univariate two-sample test using incomplete E-statistics
 x1 <- rnorm(200)
 x2 <- rnorm(300, .5)
 eqdist.etest(c(x1, x2), c(200, 300), incomplete=TRUE, N=100)

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