Revisiting Whittaker-Henderson Smoothing

Introduced nearly a century ago, Whittaker-Henderson smoothing is still widely used by actuaries for constructing one-dimensional and two-dimensional experience tables for mortality, disability and other Life Insurance risks. Our paper reframes this smoothing technique within a modern statistical framework and addresses six questions of practical relevance regarding its use.Firstly, we adopt a Bayesian view of this smoothing method to build credible intervals. Next, we shed light on the choice of the observation and weight vectors to which the smoothing should be applied by linking it to a maximum likelihood estimator introduced in the context of duration models. We then enhance the precision of the smoothing by relaxing an implicit asymptotic normal approximation on which it relies. Afterward, we select the smoothing parameters based on maximizing a marginal likelihood function. We later improve numerical performance in the presence of many observation points and consequently parameters. Finally, we extrapolate the results of the smoothing while preserving, through the use of constraints, consistency between estimated and predicted values.