Graphical goodness-of-fit test for mortality models

ABSTRACT

Candidate parametric mortality models are tested graphically. If the model is correct, the transformed data are distributed exponentially. The graphical test is based on scale and space inference. It involves smoothing of the hazard rate and simultaneous confidence intervals. It is applied to a frailty model used to set annuity reserves. Simulation and the comparison with other non-graphical tests shows that the graphical test helps localize discrepancies of empirical data with respect to the tested model.

KEYWORDS:

• Hazard rate
• mortality data
• SAINT frailty model
• local linear kernel estimator
• SiZer
• scale and space inference

Acknowledgments

The authors are grateful to two reviewers for constructive comments. We use the software R (R Core Team, 2016) for all computations.

Additional information

Funding

María Dolores Martinez-Miranda acknowledges support from the Spanish Ministry of Economy and Competitiveness, through grants MTM2013-41383P and MTM2016-76969P, which include support from the European Regional Development Fund. Rocío Raya-Miranda acknowledges support from the Spanish Ministry through grant ECO2013-48413-R of the Spanish Ministry of Economy and Competitiveness (co-financed by the European Regional Development Fund).