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Multidimensional smoothing by adaptive local kernel-weighted log-likelihood: Application to long-term care insurance

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  • Tomas, Julien
  • Planchet, Frédéric

Abstract

We are interested in modeling the mortality of long-term care (LTC) claimants having the same level of severeness (heavy claimant). Practitioners often use empirical methods that rely heavily on expert opinions. We propose approaches not depending on an expert’s advice. We analyze the mortality as a function of both the age of occurrence of the claim and the duration of the care. LTC claimants are marked by a relatively complex mortality pattern. Hence, rather than using parametric approaches or models with expert opinions, adaptive local likelihood methods allow us to extract the information from the data more pertinently. We characterize a locally adaptive smoothing pointwise method using the intersection of confidence intervals rule, as well as a global method using local bandwidth correction factors. The latter is an extension of the adaptive kernel method proposed by Gavin et al. (1995) to likelihood techniques. We vary the amount of smoothing in a location-dependent manner and allow adjustments based on the reliability of the data. Tests, and single indices summarizing the lifetime probability distribution are used to compare the graduated series obtained by adaptive local kernel-weighted log-likelihoods to p-spline and local likelihood models.

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Bibliographic Info

Article provided by Elsevier in its journal Insurance: Mathematics and Economics.

Volume (Year): 52 (2013)
Issue (Month): 3 ()
Pages: 573-589

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Handle: RePEc:eee:insuma:v:52:y:2013:i:3:p:573-589

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Web page: http://www.elsevier.com/locate/inca/505554

Related research

Keywords: Adaptive parameter choice; Local likelihood; p-splines; Long-term care insurance; Graduation; Choix adaptif des paramètres; Vraisemblance locale; p-splines; Assurance dépendance; Graduation;

References

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  1. Levantesi, Susanna & Menzietti, Massimiliano, 2012. "Managing longevity and disability risks in life annuities with long term care," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 391-401.
  2. Eilers, Paul H.C. & Currie, Iain D. & Durban, Maria, 2006. "Fast and compact smoothing on large multidimensional grids," Computational Statistics & Data Analysis, Elsevier, vol. 50(1), pages 61-76, January.
  3. Jianqing Fan & Theo Gasser & Irène Gijbels & Michael Brockmann & Joachim Engel, 1997. "Local Polynomial Regression: Optimal Kernels and Asymptotic Minimax Efficiency," Annals of the Institute of Statistical Mathematics, Springer, vol. 49(1), pages 79-99, March.
  4. Denis Kessler, 2008. "The Long-Term Care Insurance Market," The Geneva Papers on Risk and Insurance - Issues and Practice, Palgrave Macmillan, vol. 33(1), pages 33-40, January.
  5. Gavin, John & Haberman, Steven & Verrall, Richard, 1993. "Moving weighted average graduation using kernel estimation," Insurance: Mathematics and Economics, Elsevier, vol. 12(2), pages 113-126, April.
  6. Stefan Lang & Nikolaus Umlauf, 2010. "Applications of Multilevel Structured Additive Regression Models to Insurance Data," Working Papers 2010-01, Faculty of Economics and Statistics, University of Innsbruck, revised Jan 2010.
  7. Frédéric Planchet & Pascal Winter, 2007. "L'utilisation des splines bidimensionnels pour l'estimation de lois de maintien en arrêt de travail," Post-Print hal-00443004, HAL.
  8. Marie-Pascale Deléglise & Christian Hess & Sébastien Nouet, 2009. "Tarification, Provisionnement Et Pilotage D'Un Portefeuille Dépendance," Post-Print halshs-00653427, HAL.
  9. Czado, Claudia & Rudolph, Florian, 2002. "Application of survival analysis methods to long-term care insurance," Insurance: Mathematics and Economics, Elsevier, vol. 31(3), pages 395-413, December.
  10. I. D. Currie & M. Durban & P. H. C. Eilers, 2006. "Generalized linear array models with applications to multidimensional smoothing," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 68(2), pages 259-280.
  11. J.-F. Dartigues & L. Letenneur & P. Barberger-Gateau & D. Commenges & F. Gauzère, 1999. "Maladie et dépendance : description des évolutions par des modèles multi-états," Population (french edition), Institut National d'Études Démographiques (INED), vol. 54(2), pages 205-222.
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