Graphical Diagnostic for Mortality Data Modeling

The main contribution of this paper is to develop a graphical tool to evaluate the suitability of a candidate parametric model to fit a data set. The practical motivation is to check the adequacy of the so called SAINT model proposed in Jarner and Kryger (2011). This model has been implemented in practice by an important European pension fund concerned with setting annuity reserves for all current or former employees of Denmark. So, one particular relevant question is whether this mortality model is actually fitting old-age. Our graphical test can be described as follows. First we transform the data by means of the parametric model which is being evaluated. Should the model be correct, the transformed data will be in accordance with an Exponential distribution with rate 1. Then we construct a family of local linear hazard estimates based on the data on the transformed scale. Finally we use the statistical tool SiZer to assess the goodness-of-fit of the Exponential distribution to the data on the transformed scale. If the model is correct the SiZer map should not reveal any significant feature in the family of kernel estimates. Our method allow us to establish a diagnostic regarding the validity of the SAINT model when describing mortality patterns in four different countries.