Bootstrap Techniques for Mortality Models

Biostatisticians, actuaries and demographers are interested in accurately finding the age specific mortality pattern of a population. Certain different approaches have been proposed in the literature for representing the mortality of a population. Among them laws of mortality assuming a specific functional parametrization for the mortality rates have become popular in recent years mainly because of the existence of computers to handle the vast number of computations needed. The uncertainty of such a functional representation has been overlooked. The researcher is interested in both the uncertainty on the parameters and the uncertainty on the curve itself. The former provides information for specific parts of the curve that directly correspond to certain parameters while the latter allows for comparisons over time or space. Manipulation of the uncertainty can be very helpful for prediction purposes. A bootstrap approach is described, as an alternative to standard inferential methods based on asymptotic standard error theory. Such an approach can provide standard errors for both the parameters and the curve as well as it can be used for direct comparison of different curves over time or space. Application to empirical data from Sweden is also provided.