Bootstrap Techniques for Mortality Models

Abstract

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.

Modeling fertility in modern populations

“…Furthermore the classical asymptotic standard errors provided by statistical software can be quite misleading since they carry out systematic errors. An alternative solution in order to overcome the problems related to the calculations involved in asymptotic standard errors is to estimate the standard errors of the parameters of the evaluated models by utilization of a bootstrap approach as described in Karlis and Kostaki (2002).…”

Support Vector Machines as tools for mortality graduation

“…Parametric modeling is widely used in demography for graduation purposes since it provides results with the highest degree of smoothness. Detailed presentations of the features of parametric models are given by Keyfitz (1982), Kostaki (1992), Congdon (1993), and Karlis and Kostaki (2000). A huge variety of mortality laws has been presented in the literature since 1725.…”

“…Keyfitz (1982) provides a review of these historical laws. In modern times, many authors have contributed to the theory of parametric models of mortality, and to the problem of estimating their parameters (e.g., Heligman and Pollard 1980;Keyfitz 1982;Forfar et al 1988;Kostaki 1992;Hannerz 1999; Karlis and Kostaki 2000).…”

Selecting stochastic mortality models for the Italian population

“…In this regard, it is noteworthy the use of Bootstrap technique in a mortality context (see Karlis and Kostaki 2001;Brouhns et al 2005;D'amato et al 2011).…”