IDEAS home Printed from https://ideas.repec.org/a/eee/insuma/v108y2023icp177-189.html
   My bibliography  Save this article

Nonparametric density estimation and risk quantification from tabulated sample moments

Author

Listed:
  • 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," Insurance: Mathematics and Economics, Elsevier, vol. 108(C), pages 177-189.
    • Handle: RePEc:eee:insuma:v:108:y:2023:i:c:p:177-189
    DOI: 10.1016/j.insmatheco.2022.12.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167668722001275
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.insmatheco.2022.12.004?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Reynkens, Tom & Verbelen, Roel & Beirlant, Jan & Antonio, Katrien, 2017. "Modelling censored losses using splicing: A global fit strategy with mixed Erlang and extreme value distributions," Insurance: Mathematics and Economics, Elsevier, vol. 77(C), pages 65-77.
    2. Carole Bernard & Michel Denuit & Steven Vanduffel, 2018. "Measuring Portfolio Risk Under Partial Dependence Information," Journal of Risk & Insurance, The American Risk and Insurance Association, vol. 85(3), pages 843-863, September.
    3. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-1054, July.
    4. Paul Embrechts & Marius Hofert, 2013. "A note on generalized inverses," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 77(3), pages 423-432, June.
    5. Lambert, Philippe & Eilers, Paul H.C., 2009. "Bayesian density estimation from grouped continuous data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1388-1399, February.
    6. Håvard Rue & Sara Martino & Nicolas Chopin, 2009. "Approximate Bayesian inference for latent Gaussian models by using integrated nested Laplace approximations," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 319-392, April.
    7. Jaspers, Stijn & Lambert, Philippe & Aerts, Marc, 2016. "A Bayesian approach to the semiparametric estimation of a minimum inhibitory concentration distribution," LIDAM Reprints ISBA 2016033, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    8. Bolance, Catalina & Guillen, Montserrat & Nielsen, Jens Perch, 2003. "Kernel density estimation of actuarial loss functions," Insurance: Mathematics and Economics, Elsevier, vol. 32(1), pages 19-36, February.
    9. Courtois, Cindy & Denuit, Michel, 2007. "Local Moment Matching and S-convex Extrema," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 387-404, November.
    10. R. Thompson & R. J. Baker, 1981. "Composite Link Functions in Generalized Linear Models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 30(2), pages 125-131, June.
    11. Papkov, Galen I. & Scott, David W., 2010. "Local-moment nonparametric density estimation of pre-binned data," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3421-3429, December.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ayma Anza, Diego Armando & Durbán, María & Lee, Dae-Jin & Van de Kassteele, Jan, 2016. "Modelling latent trends from spatio-temporally grouped data using composite link mixed models," DES - Working Papers. Statistics and Econometrics. WS 23448, Universidad Carlos III de Madrid. Departamento de Estadística.
    2. Daniela Castro‐Camilo & Raphaël Huser & Håvard Rue, 2022. "Practical strategies for generalized extreme value‐based regression models for extremes," Environmetrics, John Wiley & Sons, Ltd., vol. 33(6), September.
    3. Lambert, Philippe, 2021. "Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    4. Lambert, Philippe, 2011. "Smooth semiparametric and nonparametric Bayesian estimation of bivariate densities from bivariate histogram data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 429-445, January.
    5. Lambert, Philippe & Gressani, Oswaldo, 2022. "Penalty parameter selection and asymmetry corrections to Laplace approximations in Bayesian P-splines models," LIDAM Discussion Papers ISBA 2022030, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Hillebrand, Eric & Schnabl, Gunther & Ulu, Yasemin, 2009. "Japanese foreign exchange intervention and the yen-to-dollar exchange rate: A simultaneous equations approach using realized volatility," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 19(3), pages 490-505, July.
    7. Frederico Belo & Chen Xue & Lu Zhang, 2010. "Cross-sectional Tobin's Q," NBER Working Papers 16336, National Bureau of Economic Research, Inc.
    8. Bansal, Ravi & Kiku, Dana & Yaron, Amir, 2016. "Risks for the long run: Estimation with time aggregation," Journal of Monetary Economics, Elsevier, vol. 82(C), pages 52-69.
    9. Alfonso Mendoza-Velázquez & Luis Carlos Ortuño-Barba & Luis David Conde-Cortés, 2022. "Corporate governance and firm performance in hybrid model countries," Review of Accounting and Finance, Emerald Group Publishing Limited, vol. 21(1), pages 32-58, February.
    10. Chang, Jinyuan & Chen, Song Xi & Chen, Xiaohong, 2015. "High dimensional generalized empirical likelihood for moment restrictions with dependent data," Journal of Econometrics, Elsevier, vol. 185(1), pages 283-304.
    11. Kutuk, Yasin, 2022. "Inequality convergence: A world-systems theory approach," Structural Change and Economic Dynamics, Elsevier, vol. 63(C), pages 150-165.
    12. Smoluk, H. J. & Neveu, Raymond P., 2002. "Consumption and asset prices: An analysis across income groups," Review of Financial Economics, Elsevier, vol. 11(1), pages 47-62.
    13. Bruce N. Lehmann, 2005. "The Role of Beliefs in Inference for Rational Expectations Models," NBER Working Papers 11758, National Bureau of Economic Research, Inc.
    14. Aslan, Alper & Kaplan, Muhittin & Kula, Ferit, 2008. "International Tourism Demand for Turkey: A Dynamic Panel Data Approach," MPRA Paper 10601, University Library of Munich, Germany.
    15. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    16. de Mendonça, Helder Ferreira & Tiberto, Bruno Pires, 2014. "Public debt and social security: Level of formality matters," Economic Modelling, Elsevier, vol. 42(C), pages 490-507.
    17. Alessandra Canepa & Fawaz Khaled, 2018. "Housing, Housing Finance and Credit Risk," IJFS, MDPI, vol. 6(2), pages 1-23, May.
    18. Isaiah Andrews & Anna Mikusheva, 2016. "Conditional Inference With a Functional Nuisance Parameter," Econometrica, Econometric Society, vol. 84, pages 1571-1612, July.
    19. Carrión-Flores, Carmen E. & Innes, Robert, 2010. "Environmental innovation and environmental performance," Journal of Environmental Economics and Management, Elsevier, vol. 59(1), pages 27-42, January.
    20. repec:ebl:ecbull:v:3:y:2007:i:44:p:1-6 is not listed on IDEAS
    21. Jessica M. Mc Lay & Roy Lay-Yee & Barry J. Milne & Peter Davis, 2015. "Regression-Style Models for Parameter Estimation in Dynamic Microsimulation: An Empirical Performance Assessment," International Journal of Microsimulation, International Microsimulation Association, vol. 8(2), pages 83-127.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:insuma:v:108:y:2023:i:c:p:177-189. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/inca/505554 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.