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The Stratified Sampling Bootstrap for Measuring the Uncertainty in Mortality Forecasts

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  • Valeria D’Amato

    (University of Salerno)

  • Steven Haberman

    (City University)

  • Maria Russolillo

    (University of Salerno)

Abstract

In this paper, we propose a procedure for reducing the uncertainty in mortality projections, on the basis of a log bilinear Poisson Lee Carter model (Renshaw and Haberman Appl Stat 52:119–137, 2003a). In the literature, because the non-linear nature of the quantities under consideration has prevented analytical solutions, simulation techniques have been used in order to provide prediction intervals for forecasted quantities (for example, Brouhns et al. Scand Actuar J 3:212–224, 2005, Renshaw and Haberman Insur Math Econ 42:797–816, 2008). In this respect, we adopt the bootstrap simulation approach in order to measure the uncertainty affecting mortality projections. In particular, we propose making the bootstrap procedure more efficient by using a specific variance reducing technique, the so-called Stratified Sampling technique. To this end, we propose a two stage simulation bootstrap procedure where variance reducing techniques are combined with the simple bootstrap of the Poisson Lee Carter version. Numerical applications are shown using the results for some datasets.

Suggested Citation

  • Valeria D’Amato & Steven Haberman & Maria Russolillo, 2012. "The Stratified Sampling Bootstrap for Measuring the Uncertainty in Mortality Forecasts," Methodology and Computing in Applied Probability, Springer, vol. 14(1), pages 135-148, March.
    • Handle: RePEc:spr:metcap:v:14:y:2012:i:1:d:10.1007_s11009-011-9225-z
    DOI: 10.1007/s11009-011-9225-z
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    References listed on IDEAS

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    1. Koissi, Marie-Claire & Shapiro, Arnold F. & Hognas, Goran, 2006. "Evaluating and extending the Lee-Carter model for mortality forecasting: Bootstrap confidence interval," Insurance: Mathematics and Economics, Elsevier, vol. 38(1), pages 1-20, February.
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    5. Renshaw, A.E. & Haberman, S., 2008. "On simulation-based approaches to risk measurement in mortality with specific reference to Poisson Lee-Carter modelling," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 797-816, April.
    6. Hyndman, Rob J. & Shahid Ullah, Md., 2007. "Robust forecasting of mortality and fertility rates: A functional data approach," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4942-4956, June.
    7. Pitacco, Ermanno & Denuit, Michel & Haberman, Steven & Olivieri, Annamaria, 2009. "Modelling Longevity Dynamics for Pensions and Annuity Business," OUP Catalogue, Oxford University Press, number 9780199547272.
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    Cited by:

    1. Hamid Mohtadi & Bryan S. Weber, 2021. "Catastrophe And Rational Policy: Case Of National Security," Economic Inquiry, Western Economic Association International, vol. 59(1), pages 140-161, January.

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