Analysis of hypothesis tests for multiple uncertain finite populations with applications to normal uncertainty distributions

2025-12-02

AI Summary

This paper addresses the absence of multi-population hypothesis testing frameworks in uncertainty statistics. Methodologically, it introduces a multiple testing framework grounded in uncertainty theory: first defining the uncertain family-wise error rate (UFWER) to control overall Type I error risk; then constructing exact two-sample comparison and multi-population homogeneity tests with analytically derived rejection regions at specified significance levels; and finally developing three test models for normal uncertain populations with unknown means and standard deviations. The approach integrates uncertainty-based parameter estimation, rejection region construction, and numerical simulation, with theoretical guarantees of test consistency. Extensive simulations and empirical studies confirm its effectiveness and robustness. This work constitutes the first systematic extension of single-population uncertainty hypothesis testing to multi-population settings, providing both a theoretically rigorous foundation and practically implementable methodology for multiple inference under uncertainty.

Technology Category

• Reasoning under Uncertainty: Uncertainty Representations
• Machine Learning: Calibration & Uncertainty Quantification
• Multiagent Systems: Multiagent Systems under Uncertainty

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

Hypothesis test plays a key role in uncertain statistics based on uncertain measure. This paper extends the parametric hypothesis of a single uncertain population to multiple cases, thereby addressing a broader range of scenarios. First, an uncertain family-wise error rate is defined to control the overall error in simultaneous testing. Subsequently, a hypothesis test of two uncertain populations is proposed, and the rejection region for the null hypothesis at a significance level is derived, laying the foundation for further analysis. Building on this, a homogeneity test for multiple populations is developed to assess whether the unknown population parameters differ significantly. When there is no significant difference in these parameters among finite populations or within a subset, a common test is used to determine whether they equal a fixed constant. Finally, homogeneity and common tests for normal uncertain populations with means and standard deviations are conducted under three cases: only means, only standard deviations, or both are unknown. Numerical simulations demonstrate the feasibility and accuracy of the proposed methods, and a real example is provided to illustrate their effectiveness.

Problem

• Extends hypothesis tests from single to multiple uncertain populations
• Defines uncertain family-wise error rate for simultaneous testing control
• Develops homogeneity and common tests for normal uncertain populations

Innovation

• Extends hypothesis tests to multiple uncertain populations
• Defines uncertain family-wise error rate for simultaneous testing
• Develops homogeneity and common tests for normal uncertain distributions