Using the Variation Coefficient for Adaptive Discrete Beta Kernel Graduation

Various approaches have been proposed in literature for the kernel graduation of mortality rates.This paper focuses on the discrete beta kernel estimator, proposed in Mazza and Punzo (2011)which pragmatically considers the age as a discrete variable and which is conceived to naturallyreduce boundary bias. Here, an attempt to improve its performance is provided. Firstly, we suggesta preliminary transformation of the data that helps to stabilize the variance and to reduce thecurvature. Secondly, we allow the smoothing parameter to vary with age according to thereliability of the data measured via the reciprocal of the variation coefficient which is function ofboth the amount of exposure and the observed mortality rate. A formulation suggested in Gavin etal. (1995) is used for the local smoothing parameter.