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Parsimonious parameterization of age-period-cohort models by Bayesian shrinkage. (English) Zbl 1390.62226

Summary: Age-period-cohort models used in life and general insurance can be over-parameterized, and actuaries have used several methods to avoid this, such as cubic splines. Regularization is a statistical approach for avoiding over-parameterization, and it can reduce estimation and predictive variances compared to MLE. In Markov Chain Monte Carlo (MCMC) estimation, regularization is accomplished by the use of mean-zero priors, and the degree of parsimony can be optimized by numerically efficient out-of-sample cross-validation. This provides a consistent framework for comparing a variety of regularized MCMC models, such as those built with cubic splines, linear splines (as ours is), and the limiting case of non-regularized estimation. We apply this to the multiple-trend model of A. Hunt and D. Blake [“A general procedure for constructing mortality models”, North Am. Actuar. J. 18, No. 1, 116–138 (2014; doi:10.1080/10920277.2013.852963)].

MSC:

62P05 Applications of statistics to actuarial sciences and financial mathematics
62J07 Ridge regression; shrinkage estimators (Lasso)
91B30 Risk theory, insurance (MSC2010)
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