Many countries have implemented social programmes providing long-term financial or in-kind entitlements. These programmes often focus on specific age-groups and consequently their expenditure streams are subject to demographic change. Given the strains already existing on public budgets,...

We propose a new generic method ROPES (Regularized Optimization for Prediction and Estimation with Sparse data) for decomposing, smoothing and forecasting two-dimensional sparse data. In some ways, ROPES is similar to Ridge Regression, the LASSO, Principal Component Analysis (PCA) and...

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...