Graduation by Adaptive Discrete Beta Kernels

arious 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 (New perspectives in statistical modeling and data analysis, studies in classification, data analysis and knowledge organization, Springer, Berlin/Heidelberg, 2011), which is conceived to naturally reduce boundary bias and in which age is pragmatically considered as a discrete variable. Here, an attempt to improve its performance is provided by allowing the bandwidth to vary with age according to the reliability of the data expressed by the amount of exposure. A formulation suggested in Gavin et al. (Trans Soc Actuaries 47:173-209, 1995) is used for the local bandwidth. A simulation study is accomplished to evaluate the gain in performance of the local bandwidth estimator with respect to the fixed bandwidth one, and an application to mortality data from the Sicily Region (Italy) for the year 2008 is finally presented.