Modelling mortality over age and time, and age and cohort: a nonparametric approach

The talk gives a gentle, albeit complete introduction to a nonparametric approach for modelling mortality over age and time, as well as over age and cohort. Specifically, mortality developments normally show regular patterns, so smoothing approaches are a natural choice to analyze mortality changes. Moreover smoothed one- and two-dimensional trends can then be used for further analysis. Though the talk places specific emphasis on P-spline models, a gradual journey toward such methods is offered. A first part is devoted to the intuitive and plain direct smoothing, using simple, self-explanatory examples. The talk then moves on to the idea of penalty, which will be crucial in setting up more sophisticated methods. Starting from simple regression problems, P-splines are presented as a flexible and versatile methodology to smooth aggregate mortality data. Specifically P-spline models combine (fixed-knot) B-splines with a roughness penalty. A relatively large number of B-splines provide enough flexibility to capture trends. The additional penalty reduces the number of parameters leading to a rather parsimonious model with smoothed trends. An important advantage of the P-spline lies in its straightforward generalization when data are presented in a rectangular array. This is the case of mortality over age and either years or cohorts. Moving between these two data structures (age vs. years and age vs. cohort) can be achieved by simple manipulation of the data without changing the general architecture of the methodology. Finally, examples of these settings will be presented.Fundación BBVAN