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Nonparametric graduation techniques as a common framework for the description of demographic patterns

Figure 21. Observed and estimated age-specific fertility rates, Finland, Figure 22. Observed and estimated age-specific nuptiality rates,
females, 1993. Ireland, males, 1998.

In addition, the SVM method produces results closer to the empirical rates in most cases, showing
a successful performance for the graduation of empirical rates in both simple and distorted data sets.
It can be observed in the figures that the results provided by SVM were closer to the empirical data
than those of most alternative methods, especially for ages in the peak and the tails of nuptiality and
fertility.
Nonparametric graduation techniques have the advantage of being suitable to all data sets. This is
an important remark, as for data sets with distorted patterns; the use of standard parametric models is
inadequate. Another advantage of the nonparametric approach is that the user has the possibility of
regulating the degree of smoothness and, as a consequence, choosing a degree adapted to the goal of
the graduation framework, avoiding in many cases oversimplification of age patterns.
As a future extension of the current work, we propose the use of SVM as a multivariate model for
demographic forecasting.

Conflict of Interest and Funding
No conflict of interest has been reported by the authors. This research is partially financed by the
Research Centre of Athens University of Economics and Business, in the framework of the project
entitled “Οriginal Scientific Publications”; and projects GROMA (MTM2015-63710-P), PPI
(RTC-2015-3580-7), and UNIKO (RTC-2015-3521-7), funded by the Ministry of Economy and
Competitiveness (Spain).

Acknowledgements
We would like to thank the editor and the reviewers for their constructive comments and their valu-
able insight, which led to significant improvements.
References

Aronszajn N. (1950). Theory of reproducing kernels. Transactions of the American Mathematical Society, 68:

18 International Journal of Population Studies | 2016, Volume 2, Issue 1