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.

翻译：Whittaker-Henderson平滑方法问世近一个世纪，至今仍是精算师构建死亡率及其他寿险风险一维和二维经验表最常用的方法之一。本文提出在现代统计框架下重新阐释该平滑技术，并回答六个与之相关的实践问题。首先，我们采用贝叶斯视角构建该平滑方法的可信区间。其次，通过将平滑方法与在持续时间模型背景下引入的最大似然估计量相关联，阐明了应应用平滑的观测向量和权重的选择。随后，通过放松其所依赖的隐式渐近近似，提升了平滑的精度。接着，我们基于边际似然最大化来选择平滑参数。之后，在存在大量观测点及相应参数的情况下，改善了数值计算性能。最后，我们通过使用约束条件保持估计值与预测值之间的一致性，对平滑结果进行了外推。