DataSimilarity (version 0.3.0)

ZC: Maxtype Edge-Count Test

Description

Performs the maxtype edge-count two-sample test for multivariate data proposed by Zhang and Chen (2017). The implementation here uses the g.tests implementation from the gTests package.

Usage

ZC(X1, X2, dist.fun = stats::dist, graph.fun = MST5, n.perm = 0, 
    dist.args = NULL, graph.args = NULL, maxtype.kappa = 1.14, seed = NULL)

Value

An object of class htest with the following components:

statistic

Observed value of the test statistic

p.value

Asymptotic or permutation p value

alternative

The alternative hypothesis

method

Description of the test

data.name

The dataset names

Details

The test is an enhancement of the Friedman-Rafsky test (original edge-count test) that aims at detecting both location and scale alternatives and is more flexible than the generalized edge-count test of Chen and Friedman (2017). The test statistic is the maximum of two statistics. The first statistic ist the weighted edge-count statistic multiplied by a factor \(\kappa\). The second statistic is the absolute value of the standardized difference of edge-counts within the first and within the second sample.

Low values of the test statistic indicate similarity of the datasets. Thus, the null hypothesis of equal distributions is rejected for high values.

For n.perm = 0, an asymptotic test using the asymptotic normal approximation of the null distribution is performed. For n.perm > 0, a permutation test is performed.

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

References

Zhang, J. and Chen, H. (2022). Graph-Based Two-Sample Tests for Data with Repeated Observations. Statistica Sinica 32, 391-415, tools:::Rd_expr_doi("10.5705/ss.202019.0116").

Chen, H., and Zhang, J. (2017). gTests: Graph-Based Two-Sample Tests. R package version 0.2, https://CRAN.R-project.org/package=gTests.

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

See Also

FR for the original edge-count test, CF for the generalized edge-count test, CCS for the weighted edge-count test, gTests for performing all these edge-count tests at once, SH for performing the Schilling-Henze nearest neighbor test, CCS_cat, FR_cat, CF_cat, ZC_cat, and gTests_cat for versions of the test for categorical data

Examples

set.seed(1234)
# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform maxtype edge-count test
if(requireNamespace("gTests", quietly = TRUE)) {  
  # Using 5-MST
  ZC(X1, X2)
  # Using 3-MST
  ZC(X1, X2, graph.fun = MST, graph.args = list(K = 3))
}