Quotation Fissler, Tobias, Pesenti, Silvana M. 2022. Sensitivity Measures Based on Scoring Functions.




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 and applications to a non-linear insurance portfolio.


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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Working/discussion paper, preprint
Language English
Title Sensitivity Measures Based on Scoring Functions
Year 2022
URL https://doi.org/10.48550/arXiv.2203.00460
JEL C52, C44, G22, C14


Fissler, Tobias (Details)
Pesenti, Silvana M. (University of Toronto, Canada)
Institute for Statistics and Mathematics IN (Details)
Research areas (Ă–STAT Classification 'Statistik Austria')
1117 Actuarial mathematics (Details)
1121 Operations research (Details)
1162 Statistics (Details)
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