BMG: Biswas et al. (2014) two-sample run test

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

Biswas et al. (2014) two-sample run test

Description

The function implements the Biswas, Mukhopadhyay and Gosh (2014) distribution-free two-sample run test. This test uses a heuristic approach to calculate the shortest Hamilton path between the two datasets using the HamiltonPath function. By default the asymptotic version of the test is calculated.

Usage

BMG(X1, X2, seed = 42, asymptotic = TRUE)

Arguments

X1	First dataset as matrix or data.frame
X2	Second dataset as matrix or data.frame
seed	Random seed (default: 42)
asymptotic	Should the asymptotic version of the test be performed (default: TRUE)

Details

The test counts the number of edges in the shortest Hamilton path calculated on the pooled sample that connect points from different samples, i.e.

T_{m,n} = 1 + \sum_{i = 1}^{N-1} U_i,

where U_i is an indicator function with U_i = 1 if the ith edge connects points from different samples and U_i = 0 otherwise.

For a combined sample size N smaller or equal to 1030, the exact version of the Biswas, Mukhopadhyay and Gosh (2014) test can be calculated. It uses the univariate run statistic (Wald and Wolfowitz, 1940) to calculate the test statistic. For N larger than 1030, the calculation for the exact version breaks.

If an asymptotic test is performed the asymptotic null distribution is given by

T_{m, n}^{*} \sim \mathcal{N}(0, 4\lambda^2(1-\lambda)^2)

where T_{m, n}^{*}= \sqrt{N} (T_{m, n} / N - 2 \lambda (1 - \lambda)) the asymptotic test statistic, \lambda = m/N and m is the sample size of the first dataset. Therefore, low absolute values of the asymptotic test statistic indicate similarity of the two datasets whereas high absolute values indicate differences between the datasets.

Value

An object of class htest with the following components:

statistic	Observed value of the test statistic (note: this is not the asymptotic test statistic)
p.value	(asymptotic) p value
method	Description of the test
data.name	The dataset names
alternative	The alternative hypothesis

Applicability

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

References

Biswas, M., Mukhopadhyay, M. and Ghosh, A. K. (2014). A distribution-free two-sample run test applicable to high-dimensional data, Biometrika 101 (4), 913-926, \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/biomet/asu045")}

Wald, A. and Wolfowitz, J. (1940). On a test whether two samples are from the same distribution, Annals of Mathematical Statistic 11, 147-162

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

HamiltonPath

Examples

# Draw some data
X1 <- matrix(rnorm(1000), ncol = 10)
X2 <- matrix(rnorm(1000, mean = 0.5), ncol = 10)
# Perform BMG test 
BMG(X1, X2)

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