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

graduation proves adequate in terms of goodness of fit. Considering the value of 4.1 quantities, these
values are lower in all female cases for SVM than for the HP model and kernels for the Swedish and
the Japanese data sets. In males, SVM are better than kernels in all cases, they are a bit higher com-
pared to the HP model for the Swedish data and in comparable levels in the French and Japanese
data sets.
Figures 1–6 illustrates the results of each technique separately for some chosen cases. It is clear in
these figures that the results of SVM are closer to the empirical data than those of HP formula, the
later exhibiting some systematic deviations in the early adult ages. It is also clear that SVM provides
smoother results than kernels. In order to do that more clearly, we compared only kernels and SVMs
(Figures 2A and 4A).

Figure 1. Empirical and graduated q x -values, French females, 1995. Figure 2. Empirical and graduated q x -values, Japanese females,
1991.

Figure 2A. Empirical and graduated q x -values, Japanese females, 1991. Figure 3. Empirical and graduated q x -values, Swedish females,
1991–1995.

5.2 Numerical Results for Fertility

In order to evaluate SVM as a tool for graduating age-specific fertility patterns, we used period

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