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The Stratified Sampling Bootstrap for Measuring the Uncertainty in Mortality Forecasts

  • Valeria D’AmatoEmail author
  • Steven Haberman
  • Maria Russolillo
Article

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.

Keywords

Lee Carter model Mortality forecasting Bootstrap Variance reducing techniques Stratified sampling 

AMS 2000 Subject Classification

62P05 

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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Valeria D’Amato
    • 1
    Email author
  • Steven Haberman
    • 2
  • Maria Russolillo
    • 1
  1. 1.Department of Economics and StatisticsUniversity of SalernoFiscianoItaly
  2. 2.Faculty of Actuarial Science and Insurance, Cass Business SchoolCity UniversityLondonUK

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