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

cent Swedish data. The bulge during the young ages appears around age 20 and the older one around
age 40. This phenomenon has also started to appear in the data sets of Finland and Ireland. In
these cases, simple models fail to closely estimate the tails and the peak value of the marriage dis-
tribution. We thus fitted the mixture model MC-M to the data sets. Figures 20–22 provide illustra-
tions of the results.
According to the values of the minimizing criterion, for the majority of the cases the C-M model
provides the best fits among the parametric models. The second best fit is usually obtained by the
GLG one.
As mentioned above, a variety of factors related to the socioeconomic and cultural background of
male and female populations may contribute to the appearance of the heterogeneity in the
first-marriage curve. However in order to be able to verify or reject all these hypotheses about het-
erogeneity in the first-marriage curve, further research based on empirical evidence is required.
Turning now to the SVM, we observed from the values of the residual sum of squares as well as
from the graphical illustration, that their performance is superior in comparison to any other para-
metric approach. In the vast majority of the data sets, the values of the residual sum of squares were
in significantly lower levels than those resulting by model fitting. It is probably worth mentioning
that this technique works with high accuracy in both homogeneous and heterogeneous data sets,
while for the later cases more complicated models are required. Taking a closer look at the figures,
we observed that SVM performance is highly superior to parametric modelling, in the peaks and the
tables of the marriage distributions where parametric modelling provides systematic deviations from
the empirical rates.

Table 4. Values of (4.3), multiplied by 100.000, at the exit of the estimation procedure
FEMALES
SSE*10 6 Standard Coale-McNeil GLG Coale-McNeil Kernel SVM
Spain
1995 62308 17358 14058 788 216
2002 46959 14321 12446 731 185
Greece
2001 54891 8333 63228 331 214
2002 54891 8333 63228 289 329
Italy
1990 38956 8654 8251 2431 2706
2000 47607 8605 6597 603 312
Germany
1998 27263 4936 4761 786 517
2001 19583 3331 3137 279 195
Netherlands
1996 19516 2661 2563 859 1144
2002 40108 8705 8171 372 201
Norway
1996 29525 8001 7828 1746 3986
2002 20803 5770 5291 352 539
UK
1996 12060 2271 2226 449 223
1999 214910 10280 10278 759 241

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