The stratified sampling bootstrap for measuring the uncertainty in mortality forecasts. (English) Zbl 1362.62182

Summary: 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 [A. Renshaw and S. Haberman, J. R. Stat. Soc., Ser. C, Appl. Stat. 52, No. 1, 119–137 (2003; Zbl 1111.62359)]. 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, N. Brouhns et al. [Scand. Actuar. J. 2005, No. 3, 212–224 (2005; Zbl 1092.91038)], A. Renshaw and S. Haberman, Insur. Math. Econ. 42, No. 2, 797–816 (2008; Zbl 1152.91598)]. 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.


62P05 Applications of statistics to actuarial sciences and financial mathematics
62D05 Sampling theory, sample surveys
62F40 Bootstrap, jackknife and other resampling methods
62M20 Inference from stochastic processes and prediction
91B30 Risk theory, insurance (MSC2010)
91B82 Statistical methods; economic indices and measures
92B15 General biostatistics
Full Text: DOI


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