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Sensitivity Measures Based on Scoring Functions

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  • Tobias Fissler
  • Silvana M. Pesenti

Abstract

We propose a holistic framework for constructing sensitivity measures for any elicitable functional $T$ of a response variable. The sensitivity measures, termed score-based sensitivities, are constructed via scoring functions that are (strictly) consistent for $T$. These score-based sensitivities quantify the relative improvement in predictive accuracy when available information, e.g., from explanatory variables, is used ideally. We establish intuitive and desirable properties of these sensitivities and discuss advantageous choices of scoring functions leading to scale-invariant sensitivities. Since elicitable functionals typically possess rich classes of (strictly) consistent scoring functions, we demonstrate how Murphy diagrams can provide a picture of all score-based sensitivity measures. We discuss the family of score-based sensitivities for the mean functional (of which the Sobol indices are a special case) and risk functionals such as Value-at-Risk, and the pair Value-at-Risk and Expected Shortfall. The sensitivity measures are illustrated using numerous examples, including the Ishigami--Homma test function. In a simulation study, estimation of score-based sensitivities for a non-linear insurance portfolio is performed using neural nets.

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  • Tobias Fissler & Silvana M. Pesenti, 2022. "Sensitivity Measures Based on Scoring Functions," Papers 2203.00460, arXiv.org, revised Jul 2022.
    • Handle: RePEc:arx:papers:2203.00460
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    References listed on IDEAS

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    Cited by:

    1. Silvana M. Pesenti, 2022. "Reverse Sensitivity Analysis for Risk Modelling," Risks, MDPI, vol. 10(7), pages 1-23, July.
    2. Tobias Fissler & Hajo Holzmann, 2022. "Measurability of functionals and of ideal point forecasts," Papers 2203.08635, arXiv.org.
    3. Anthony Coache & Sebastian Jaimungal & 'Alvaro Cartea, 2022. "Conditionally Elicitable Dynamic Risk Measures for Deep Reinforcement Learning," Papers 2206.14666, arXiv.org, revised May 2023.

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