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Sensitivity measures based on scoring functions
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DOI：10.1016/j.ejor.2022.10.002.png)
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Abstract
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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 improve-ment 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 Short-fall. 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.(c) 2022 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY license ( http://creativecommons.org/licenses/by/4.0/ )
Keywords:
Consistency
Elicitability
Expected shortfall
Information value
Value -at -Risk
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