DISCOF: Distance Components (DISCO) Tests

In DataSimilarity: Quantifying Similarity of Datasets and Multivariate Two- And k-Sample Testing

Distance Components (DISCO) Tests

Description

Performs Energy statistics distance components (DISCO) multi-sample tests (Rizzo and Székely, 2010). The implementation here uses the disco implementation from the energy package.

Usage

DISCOF(X1, X2, ..., n.perm = 0, alpha = 1, seed = 42)

Arguments

X1	First dataset as matrix or data.frame
X2	Second dataset as matrix or data.frame
...	Further datasets as matrices or data.frames
n.perm	Number of permutations for Bootstrap test (default: 0, no Bootstrap test performed)
alpha	Power of the distance used for generalized Energy statistic (default: 1). Has to lie in (0,2]. For values in (0, 2), consistency of the resulting test has been shown.
seed	Random seed (default: 42)

Details

DISCO is a method for multi-sample testing based on all pairwise between-sample distances. It is analogous to the classical ANOVA. Instead of decomposing squared differences from the sample mean, the total dispersion (generalized Energy statistic) is composed into distance components (DISCO) consisting of the within-sample and between-sample measures of dispersion.

DISCOF is based on the DISCO F ratio of the between-sample and within-sample dispersion. Note that the F ration does not follow an F distribution, but is just called F ratio analogous to the ANOVA.

In both cases, small values of the statistic indicate similarity of the datasets and therefore, the null hypothesis of equal distributions is rejected for large values of the statistic.

This implementation is a wrapper function around the function disco that modifies the in- and output of that function to match the other functions provided in this package. For more details see the disco.

Value

An object of class disco with the following components:

call	The function call
method	Description of the test
statistic	Vector of observed values of the test statistic
p.value	Vector of Bootstrap p values
k	Number of samples
N	Number of observations
between	Between-sample distance components
withins	One-way within-sample distance components
within	Within-sample distance component
total	Total dispersion
Df.trt	Degrees of freedom for treatments
Df.e	Degrees of freedom for error
index	Alpha (exponent on distance)
factor.names	Factor names
factor.levels	Factor levels
sample.sizes	Sample sizes
stats	Matrix containing decomposition

Applicability

Target variable?	Numeric?	Categorical?	K-sample?
No	Yes	No	Yes

References

Szekely, G. J. and Rizzo, M. L. (2004) Testing for Equal Distributions in High Dimension, InterStat, November (5).

Rizzo, M. L. and Szekely, G. J. (2010). DISCO Analysis: A Nonparametric Extension of Analysis of Variance, Annals of Applied Statistics, 4(2), 1034-1055. doi:10.1214/09-AOAS245

Szekely, G. J. (2000) Technical Report 03-05: E-statistics: Energy of Statistical Samples, Department of Mathematics and Statistics, Bowling Green State University.

Rizzo, M., Szekely, G. (2022). energy: E-Statistics: Multivariate Inference via the Energy of Data. R package version 1.7-11, https://CRAN.R-project.org/package=energy.

Stolte, M., Kappenberg, F., Rahnenführer, J., Bommert, A. (2024). Methods for quantifying dataset similarity: a review, taxonomy and comparison. Statist. Surv. 18, 163 - 298. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/24-SS149")}

See Also

DISCOB, Energy

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform DISCO tests
if(requireNamespace("energy", quietly = TRUE)) {
  DISCOF(X1, X2, n.perm = 100)
}

DataSimilarity documentation built on April 3, 2025, 9:39 p.m.