  Introduced nearly a century ago, Whittaker-Henderson smoothing remains one of
the most commonly used methods by actuaries for constructing one-dimensional
and two-dimensional experience tables for mortality and other Life Insurance
risks. This paper proposes to reframe this smoothing technique within a modern
statistical framework and addresses six questions of practical interest
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 observation
vectors and weights 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
approximation on which it relies. Afterward, we select the smoothing parameters
based on maximizing a marginal likelihood. We later improve numerical
performance in the presence of a large number of observation points and,
consequently, parameters. Finally, we extrapolate the results of the smoothing
while preserving consistency between estimated and predicted values through the
use of constraints.

Methodology