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European Actuarial Journal
Published in: European Actuarial Journal 1/2023

11-01-2023 | Letter

Model selection with Gini indices under auto-calibration

Author: Mario V. Wüthrich

Published in: European Actuarial Journal | Issue 1/2023

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Abstract

The Gini index does not give a strictly consistent scoring function. Therefore, simply maximizing the Gini index may lead to a wrong model choice. The main issue is that the Gini index is a rank-based score that is not calibration-sensitive. We show that the Gini index allows for strictly consistent scoring if we restrict it to the class of auto-calibrated regression models. That is, on the class of auto-calibrated models we know that the true model maximizes the Gini index.
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Footnotes
1
The continuity condition is a comparably weak assumption, e.g., it suffices to have one continuous covariate component and a strictly monotone regression function in that component; see Section 2.2 of Denuit et al. [4].
 
2
In (2.2) we assume that Y has a continuous distribution \(F_Y\), otherwise the denominator in (2.2) needs to be replaced by the term \({\mathbb {E}}[|Y-Z|]/(4{\mathbb {E}}[Y])\), where Z is an independent copy of Y, see also (4.1), below. For a continuous distribution \(F_Y\) the two terms in the denominator are then equivalent.
 
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Metadata
Title
Model selection with Gini indices under auto-calibration
Author
Mario V. Wüthrich
Publication date
11-01-2023
Publisher
Springer Berlin Heidelberg
Published in
European Actuarial Journal / Issue 1/2023
Print ISSN: 2190-9733
Electronic ISSN: 2190-9741
DOI
https://doi.org/10.1007/s13385-022-00339-9

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