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International Journal of Population Studies

RESEARCH ARTICLE

Nonparametric graduation techniques as

a common framework for the description of

demographic patterns

1
2
1
3
Anastasia Kostaki , Javier M. Moguerza , Alberto Olivares and Stelios Psarakis
1 Department of Statistics, Athens University of Economics and Business, Greece
2 Department of Computer Science and Statistics, Rey Juan Carlos University, Spain
3 Department of Signal Theory and Communications and Telematic Systems and Computing, Rey Juan
Carlos University, Spain

Abstract: The graduation of age-specific demographic rates is a subject of special interest in many dis-
ciplines as demography, biostatistics, actuarial practice, and social planning. For estimating the unknown
age-specific probabilities of the various demographic phenomena, some graduation technique must be
applied to the corresponding empirical rates, under the assumption that the true probabilities follow a
smooth pattern through age. The classical way for graduating demographic rates is parametric modelling.
However, for graduation purposes, nonparametric techniques can also be adapted. This work provides an
adaptation, and an evaluation of kernels and Support Vector Machines (SVM) in the context of graduation
of demographic rates.
Keywords: graduation, mortality pattern, fertility pattern, kernels, Support Vector Machines

*Correspondence to: Anastasia Kostaki, Department of Statistics, Athens University of Economics and Business, Greece;
Email: kostaki@aueb.gr

Received: August 24, 2015; Accepted: October 4, 2015; Published Online: October 17, 2015
Citation: Kostaki A, Moguerza J M, Olivares A, et al. (2016). Nonparametric graduation techniques as a common
framework for the description of demographic patterns. International Journal of Population Studies, vol.2(1): 1–20.
http://dx.doi.org/10.18063/IJPS.2016.01.001.

1. Introduction
The graduation of demographic rates is a subject of special interest in demographic analysis, biostatistics,
actuarial practice, and social planning. The demographer needs to describe the age-specific patterns
of the various demographic phenomena in a population for various purposes such as providing
Copyright: © 2016 Anasta- population projections, constructing life tables and multiple decrement tables, as well as for calcu-
sia Kostaki, et al. This is an lating reproduction rates. The actuary needs a mortality and fertility basis suitable for calculations in
Open Access article distri-
buted under the terms of the life insurance and in designing of social security systems. Social planning also requires estimations
Creative Commons Attribution- and projections of the age-specific demographic patterns for many purposes, e.g., for designing
NonCommercial 4.0 Interna- health care systems, as well as for analysing and projecting the labour force.
tional License (http://creative-
commons.org/licenses/by-nc/ In order to estimate the unknown age-specific probabilities of the various demographic phenom-
4.0/), permitting all non-com- ena underlying the empirical age-specific rates which are affected by random fluctuations, the typi-
mercial use, distribution, and cal way is the utilization of some graduation techniques to be applied to the empirical age-specific
reproduction in any medium,
provided the original work is rates, under the assumption that the true probabilities follow a smooth pattern through age. A gradua-
properly cited. tion technique, focusing to eliminate random fluctuations affecting the empirical measures, can

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