Weighted Graph-Based Two-Sample Test via Empirical Likelihood

• Published in: Mathematics (Basel) Vol. 12; no. 17; p. 2745
• Main Authors: Zhao, Xiaofeng, Yuan, Mingao
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01-09-2024
• Subjects: Biological effects; Data analysis; empirical likelihood; Graphs; Hypotheses; Hypothesis testing; Lagrange multiplier; Networks; Nonparametric statistics; Null hypothesis; Random variables; two-sample test; weighted graph
• ISSN: 2227-7390; 2227-7390
• DOI: 10.3390/math12172745

In network data analysis, one of the important problems is determining if two collections of networks are drawn from the same distribution. This problem can be modeled in the framework of two-sample hypothesis testing. Several graph-based two-sample tests have been studied. However, the methods mainly focus on binary graphs, and many real-world networks are weighted. In this paper, we apply empirical likelihood to test the difference in two populations of weighted networks. We derive the limiting distribution of the test statistic under the null hypothesis. We use simulation experiments to evaluate the power of the proposed method. The results show that the proposed test has satisfactory performance. Then, we apply the proposed method to a biological dataset.