BQS: Barakat et al. (1996) Two-Sample Test

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

Barakat et al. (1996) Two-Sample Test

Description

Performs the nearest-neighbor-based multivariate two-sample test of Barakat et al. (1996).

Usage

BQS(X1, X2, dist.fun = stats::dist, n.perm = 0, dist.args = NULL, seed = NULL)

Arguments

X1	First dataset as matrix or data.frame
X2	Second dataset as matrix or data.frame
dist.fun	Function for calculating a distance matrix on the pooled dataset (default: stats::dist, Euclidean distance).
n.perm	Number of permutations for permutation test (default: 0, no test is performed).
dist.args	Named list of further arguments passed to dist.fun (default: NULL).
seed	Random seed (default: NULL). A random seed will only be set if one is provided.

Details

The test is an extension of the Schilling (1986) and Henze (1988) neighbor test that bypasses choosing the number of nearest neighbors to consider. The Schilling-Henze test statistic is the proportion of edges connecting points from the same dataset in a K-nearest neighbor graph calculated on the pooled sample (standardized with expectation and SD under the null). Barakat et al. (1996) take the weighted sum of the Schilling-Henze test statistics for K = 1,\dots,N-1, where N denotes the pooled sample size.

As for the Schilling-Henze test, low values of the test statistic indicate similarity of the datasets. Thus, the null hypothesis of equal distributions is rejected for high values. A permutation test is performed if n.perm is set to a positive number.

Value

An object of class htest with the following components:

statistic	Observed value of the test statistic
p.value	Permutation p value (if n.perm > 0)
alternative	The alternative hypothesis
method	Description of the test
data.name	The dataset names

Applicability

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

References

Barakat, A.S., Quade, D. and Salama, I.A. (1996), Multivariate Homogeneity Testing Using an Extended Concept of Nearest Neighbors. Biom. J., 38: 605-612. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1002/bimj.4710380509")}

Schilling, M. F. (1986). Multivariate Two-Sample Tests Based on Nearest Neighbors. Journal of the American Statistical Association, 81(395), 799-806. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.2307/2289012")}

Henze, N. (1988). A Multivariate Two-Sample Test Based on the Number of Nearest Neighbor Type Coincidences. The Annals of Statistics, 16(2), 772-783.

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

SH, FR, CF, CCS, ZC for other graph-based tests, FR_cat, CF_cat, CCS_cat, and ZC_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 Barakat et al. test
BQS(X1, X2, n.perm = 100)

DataSimilarity documentation built on June 16, 2025, 5:08 p.m.