Discrete Beta Kernel Graduation of Age-Specific Demographic Indicators
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Several approaches have been proposed in literature for the kernel graduation of age-specific demographic indicators. Nevertheless, although age is pragmatically a discretized variable with a finite support (typically age at last birthday is considered), commonly used methods employ continuous kernel functions. Moreover, symmetric kernels, that bring in further bias at the support boundaries (the so-called problem of boundary bias), are routinely adopted. In this paper we propose a discrete kernel smooth estimator specifically conceived for the graduation of discrete finite functions, such are age-specific indicators. Kernel functions are chosen from a family of conveniently discretized and re-parameterized beta densities; since their support matches the age range, the issue of boundary bias is eliminated. An application to 1999–2001 mortality data from the Valencia Region (Spain) is also presented.
KeywordsSmoothing Parameter Kernel Estimator Demographic Indicator Symmetric Kernel Beta Density
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- Copas, J. B., & Haberman, S. (1983). Non-parametric graduation using kernel methods. Journal of the Institute of Actuaries, 110, 135–156.Google Scholar
- Debòn, A., Montes, F., & Sala, R. (2005). A comparison of parametric models for mortality graduation. Application to mortality data for the Valencia region (Spain). Statistics and Operations Research Transactions, 29(2), 269–288.Google Scholar
- Gavin, J. B., Haberman, S., & Verrall, R. J. (1995). Graduation by kernel and adaptive kernel methods with a boundary correction. Transactions of the Society of Actuaries, 47, 173–209.Google Scholar
- Preston, S., Heuveline, P., & Guillot, M. (2001). Demography: Measuring and modelling population processes. Oxford: Blackwell.Google Scholar