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Anastasia Kostaki, Javier M. Moguerza, Alberto Olivares and Stelios Psarakis

∑ wq x q x ) 2 (4.1)
( ˆ −
x
x
With weights w x the reciprocals of the estimated variances of the age-specific mortality rates
w = E x / q x (1 q− x ) , where E x is the exposed-to-risk population at age x and q x is the mortality rate
x

at age x.
For the SVM applications, the subroutine “svm” of the library e1071 for the R-package is used for
the derivation of the SVM model parameters. This is available from http://cran.r-project.org/. In or-
der to select the parameters ε, σ, and C for the ε-regression procedure, the previously
tioned cross-validation technique was conducted. Since the search within the grid of parameters in-
volves randomness, for the sake of replicability, we provided the final combination of parameters
used in the experiments. In particular, the values ε= 0.02, σ = 125 and C = 2200 have been chosen
for this SVM implementation.
Although the graphical representation of the observed and the graduated rates is a useful way for
deriving conclusions, we also used a statistical criterion in order to evaluate the performance of the
alternative estimators. To check the closeness of the graduated rates to the observed ones, we used
2
the χ criterion, (4.1) that was used as minimizing criterion for fitting HP model.
The values of the criterion (4.1) for all the data sets used, and all the graduation techniques ap-
plied, are presented in Table 1. Examining these values, one can easily observe that the SVM

Table 1. Values of (4.1) at the exit of the estimation procedure for HP, SVM, and Kernels
Sweden
HP SVM Kernels
Females
1981–1985 950 725 2842
1984–1988 861 293 1817
1991–1995 1468 882 2507
Males
1981–1985 180 717 3813
1984–1988 191 485 3125
1991–1995 268 490 3340
Japan
Females
1990 4370 453 1767
1991 3849 568 1859
1995 3516 320 1601
Males
1990 1140 495 2219
1991 951 300 2047
1995 542 394 2023
France
Females
1990 2887 594 3508
1991 1995 639 2897
1995 879 366 1839
Males
1990 983 786 4685
1991 687 999 4625
1995 987 1117 2697

International Journal of Population Studies | 2016, Volume 2, Issue 1 7