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平滑方法引入近一个世纪以来，仍是精算师构建一维和二维死亡率及其他寿险风险经验表时最常用的方法之一。本文提出在现代统计框架下重新诠释这一平滑技术，并解决其应用中六个具有实际意义的问题。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，通过将其与持续时间模型中引入的最大似然估计量相联系，阐明平滑应适用的观测向量和权重选择。随后，通过放宽平滑所依赖的隐含渐近近似，提高平滑精度。接着，基于边际似然最大化选择平滑参数。之后，在存在大量观测点及相应参数的情况下改进数值性能。最后，通过约束条件保持估计值与预测值之间的一致性，对平滑结果进行外推。