Discrete Beta Kernel Graduation of Age-Specific Demographic Indicators

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.