
arXiv: 2306.06932
Abstract 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.
FOS: Computer and information sciences, duration models, [STAT.ME] Statistics [stat]/Methodology [stat.ME], extrapolation, Methodology, marginal likelihood, experience tables, approche bayésienne empirique, modèles additifs généralisés, generalized additive models, Methodology (stat.ME), smoothing methods, maximum de vraisemblance, méthodes de lissage, tables d'expérience, empirical Bayes approach, vraisemblance marginale, modèles de durée, maximum likelihood
FOS: Computer and information sciences, duration models, [STAT.ME] Statistics [stat]/Methodology [stat.ME], extrapolation, Methodology, marginal likelihood, experience tables, approche bayésienne empirique, modèles additifs généralisés, generalized additive models, Methodology (stat.ME), smoothing methods, maximum de vraisemblance, méthodes de lissage, tables d'expérience, empirical Bayes approach, vraisemblance marginale, modèles de durée, maximum likelihood
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