Two-dimensional smoothing of mortality rates

We propose three new practical methods of smoothing mortality rates (the procedure known in demography as graduation) over two dimensions: age and time. The first method uses bivariate thin plate splines. The second uses a similar procedure but with lasso-type regularization. The third method also uses bivariate lasso-type regularization, but allows for both period and cohort effects. Thus the mortality rates are modelled as the sum of four components: a smooth bivariate function of age and time, smooth one-dimensional cohort effects, smooth one-dimensional period effects and random errors. Cross validation is used to compare these new methods of graduation with existing approaches.