Using the Variation Coefficient for Adaptive Discrete Beta Kernel Graduation

Various approaches have been proposed in literature for the kernel graduation of mortality rates. Among them, this paper considers, as a starting point, the fixed bandwidth discrete beta kernel estimator, a recent proposal conceived to intrinsically reduce boundary bias and in which age is pragmatically considered as a discrete variable. An adaptive variant of this estimator also exists, which allows the bandwidth to vary with age according to the reliability of the data as expressed only by the amount of exposure. This paper presents a further adaptive version, obtained by measuring the reliability via the reciprocal of the variation coefficient, which is function of both the amount of exposure and the observed mortality rates. A simulation study is accomplished to evaluate the gain in performance of the new estimator with respect to its predecessors.