caa a22 4500 605476071 CHVBK 20210128100354.0 cr unu---uuuuu 210128e20150701xx s 000 0 eng 10.1007/s10985-014-9300-1 doi (NATIONALLICENCE)springer-10.1007/s10985-014-9300-1 Bivariate discrete beta Kernel graduation of mortality data [Elektronische Daten] [Angelo Mazza, Antonio Punzo] Various parametric/nonparametric techniques have been proposed in literature to graduate mortality data as a function of age. Nonparametric approaches, as for example kernel smoothing regression, are often preferred because they do not assume any particular mortality law. Among the existing kernel smoothing approaches, the recently proposed (univariate) discrete beta kernel smoother has been shown to provide some benefits. Bivariate graduation, over age and calendar years or durations, is common practice in demography and actuarial sciences. In this paper, we generalize the discrete beta kernel smoother to the bivariate case, and we introduce an adaptive bandwidth variant that may provide additional benefits when data on exposures to the risk of death are available; furthermore, we outline a cross-validation procedure for bandwidths selection. Using simulations studies, we compare the bivariate approach proposed here with its corresponding univariate formulation and with two popular nonparametric bivariate graduation techniques, based on Epanechnikov kernels and on $$P$$ P -splines. To make simulations realistic, a bivariate dataset, based on probabilities of dying recorded for the US males, is used. Simulations have confirmed the gain in performance of the new bivariate approach with respect to both the univariate and the bivariate competitors. Springer Science+Business Media New York, 2014 Bivariate graduation nationallicence Kernel smoothing nationallicence Beta distribution nationallicence Cross-validation nationallicence Mazza Angelo Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy aut Punzo Antonio Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy aut Lifetime Data Analysis Springer US; http://www.springer-ny.com 21/3(2015-07-01), 419-433 1380-7870 21:3<419 2015 21 10985 https://doi.org/10.1007/s10985-014-9300-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10985-014-9300-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mazza Angelo Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy aut NATIONALLICENCE 700 1- Punzo Antonio Department of Economics and Business, University of Catania, Corso Italia 55, 95129, Catania, Italy aut NATIONALLICENCE 773 0- Lifetime Data Analysis Springer US; http://www.springer-ny.com 21/3(2015-07-01), 419-433 1380-7870 21:3<419 2015 21 10985