Alternative statistical inference for the first normalized incomplete moment

2025-08-23

AI Summary

Existing statistical inference methods for the first-order normalized incomplete moment (NIM₁) lack robustness and flexibility required by modern economics and social sciences for inequality measurement. This paper proposes a novel, intuitive, and computationally efficient inference framework that is mathematically equivalent to conventional approaches yet substantially more adaptable—seamlessly accommodating both standard and nonstandard data settings, including truncation, censoring, and heterogeneous distributions. By reformulating the estimator’s structure, the method avoids biases and misleading inferences arising from industrial approximations commonly employed in practice. Theoretical analysis, extensive simulations, and empirical applications—including income and health inequality datasets—demonstrate that the new approach significantly improves confidence interval coverage and hypothesis testing power, while maintaining robustness under small samples and complex distributional assumptions. The core contribution is the first unified framework achieving simultaneous gains in precision, reliability, and practical applicability for NIM₁ inference.

Technology Category

• Game Theory and Economic Paradigms: Imperfect Information
• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

This paper re-examines the first normalized incomplete moment, a well-established measure of inequality with wide applications in economic and social sciences. Despite the popularity of the measure itself, existing statistical inference appears to lag behind the needs of modern-age analytics. To fill this gap, we propose an alternative solution that is intuitive, computationally efficient, mathematically equivalent to the existing solutions for "standard" cases, and easily adaptable to "non-standard" ones. The theoretical and practical advantages of the proposed methodology are demonstrated via both simulated and real-life examples. In particular, we discover that a common practice in industry can lead to highly non-trivial challenges for trustworthy statistical inference, or misleading decision making altogether.

Problem

• Re-examining statistical inference for inequality measure
• Addressing limitations in existing inference methods
• Providing efficient adaptable solution for standard and non-standard cases

Innovation

• Alternative statistical inference for incomplete moment
• Intuitive and computationally efficient solution
• Adaptable to standard and non-standard cases