Whittaker--Henderson smoothing revisited: A modern statistical framework for practical use

Introduced over a century ago, Whittaker-Henderson smoothing remains widely used by actuaries in constructing one-dimensional and two-dimensional experience tables for mortality, disability and other life insurance risks. In this paper, we reinterpret this smoothing technique within a modern statistical framework and address six practically relevant questions about its use. First, we adopt a Bayesian perspective on this method to construct credible intervals. Second, in the context of survival analysis, we clarify how to choose the observation and weight vectors by linking the smoothing technique to a maximum likelihood estimator. Third, we improve accuracy by relaxing the method's reliance on an implicit normal approximation. Fourth, we select the smoothing parameters by maximizing a marginal likelihood function. Fifth, we improve computational efficiency when dealing with numerous observation points and consequently parameters. Finally, we develop an extrapolation procedure that ensures consistency between estimated and predicted values through constraints.