Proofs that the Gerber Statistic is Positive Semidefinite
Proofs that the Gerber Statistic is Positive Semidefinite ArXiv ID: 2305.05663 “View on arXiv” Authors: Unknown Abstract In this brief note, we prove that both forms of the Gerber statistic introduced in Gerber et al. (2022) are positive semi-definite. Keywords: Gerber Statistic, Positive Semi-Definite, Risk Management, Dependence Modeling, General (Risk Measurement) Complexity vs Empirical Score Math Complexity: 8.5/10 Empirical Rigor: 2.0/10 Quadrant: Lab Rats Why: The paper is dense with advanced linear algebra proofs, demonstrating matrix transformations and series expansions to establish positive semidefiniteness, which is a purely theoretical property with no practical implementation details provided. It contains no backtesting, datasets, or statistical metrics, focusing solely on the mathematical validity of the Gerber statistic. flowchart TD A["Research Goal<br/>Prove Gerber Statistic is PSD"] --> B["Analyze Structure<br/>1-form and 2-form"] B --> C["Mathematical Derivation<br/>Matrix Factorization & Boundaries"] C --> D["Computational Verification<br/>Symbolic/Numerical Analysis"] D --> E["Key Findings<br/>Both forms are Positive Semi-Definite"] E --> F["Outcomes<br/>Validated for Risk Management & Dependence Modeling"]