Penalized least squares smoothing of two-dimensional mortality tables with imposed smoothness

Abstract
This paper presents a method to estimate mortality trends of two-dimensional mortality tables. Comparability of mortality trends for two or more of such tables is enhanced by applying penalized least squares and imposing a desired percentage of smoothness to be attained by the trends. The smoothing procedure is basically determined by the smoothing parameters that are related to the percentage of smoothness. To quantify smoothness, we employ an index defined first for the one-dimensional case and then generalized to the two-dimensional one. The proposed method is applied to data from member countries of the OECD. We establish as goal the smoothed mortality surface for one of those countries and compare it with some other mortality surfaces smoothed with the same percentage of two-dimensional smoothness.Our aim is to be able to see whether convergence exists in the mortality trends of the countries under study, in both year and age dimensions.