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Nonparametric density estimation and risk quantification from tabulated sample moments

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  • Lambert, Philippe

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.

Suggested Citation

  • Lambert, Philippe, 2023. "Nonparametric density estimation and risk quantification from tabulated sample moments," LIDAM Reprints ISBA 2023001, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2023001
    DOI: https://doi.org/10.1016/j.insmatheco.2022.12.004
    Note: In: Insurance: Mathematics and Economics, 2023, vol. 108, p. 177-189
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    More about this item

    Keywords

    Nonparametric density estimation ; Grouped data ; Tabulated sample moments ; Value-at-Risk ; P-splines;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General

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