Asymptotic linear dependence and ellipse statistics for multivariate two-sample homogeneity test

2025-11-24

AI Summary

This paper addresses the multivariate two-sample distribution homogeneity testing problem by proposing a novel nonparametric test based on statistical depth. The method constructs a center-outward ordering of samples using statistical depth and introduces a new asymptotically linear test statistic; under the null hypothesis, this statistic converges in distribution to a chi-square distribution, circumventing the computational burden of resampling procedures. Its key innovation lies in the first integration of depth-based ordering with asymptotic linearization techniques, augmented by an elliptical statistic designed to better capture multivariate dependence structures. Extensive simulations and empirical analyses demonstrate that the proposed test maintains high finite-sample power and exhibits robustness against non-spherical distributions, high dimensionality, and heteroscedasticity. Overall, it advances both the theoretical accuracy and practical applicability of multivariate nonparametric inference.

Technology Category

• Search and Optimization: Non-convex Optimization
• Machine Learning: Multi-instance/Multi-view Learning
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for heterogeneous, signed, attributed, multi-relational, temporal, higher-order, and annotated Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods

Abstract

Statistical depth, which measures the center-outward rank of a given sample with respect to its underlying distribution, has become a popular and powerful tool in nonparametric inference. In this paper, we investigate the use of statistical depth in multivariate two-sample problems. We propose a new depth-based nonparametric two-sample test, which has the Chi-square(1) asymptotic distribution under the null hypothesis. Simulations and real-data applications highlight the efficacy and practical value of the proposed test.

Problem

• Developing a nonparametric multivariate two-sample homogeneity test
• Using statistical depth to compare distributions between two samples
• Validating test efficacy through simulations and real-data applications

Innovation

• Nonparametric test using statistical depth
• Chi-square asymptotic distribution under null
• Multivariate two-sample homogeneity test method