Nonparametric density estimation and risk quantification from tabulated sample moments
(2023) Insurance: Mathematics and Economics — Vol. 108, p. 177-189 (2023)
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- Abstract
- Continuous data such as losses are often summarized by means of histograms or displayed in tabular format: the range of data is partitioned into consecutive interval classes and the number of observations falling within each class is provided to the analyst. This paper investigates how the additional report of sample moments within each class can be integrated to obtain a smooth nonparametric estimate of the density and credible intervals for the loss quantiles. Extensive simulations confirm the merits of the proposed methodology with correctly estimated densities based on tabulated sample moments of increasing orders and effective coverages of credible intervals close to their nominal values, even when the number of classes is small. An application on motor insurance data further illustrates the usefulness of the method with an estimation of the loss density and of Value-at-Risk.
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Citations
Lambert, P. (2023). Nonparametric density estimation and risk quantification from tabulated sample moments. Insurance: Mathematics and Economics, 108, 177-189. https://doi.org/10.1016/j.insmatheco.2022.12.004 (Original work published 2023)