Statistical methods that shrink parameters towards zero can produce lower predictive variance than does maximum likelihood. This paper discusses an approach to doing this for age-period-cohort models, and applies it to fitting opioid mortality rates with a generalization of the Lee-Carter model...

Background: Bayesian regularization can address over-parameterization of age-period-cohort (APC) mortality models, facilitated by a new methodology for comparing fits of Bayesian regularized models. Here Bayesian Lasso is used to shrink slope changes in linear spline fits of the parameters of...

Smoothing splines are splines fit including a roughness penalty. They can be used across groups of variables in regression models to produce more parsimonious models with improved accuracy. For APC (age-period-cohort) models, the variables in each direction can be numbered sequentially 1:N,...

Parameter shrinkage is known to reduce fitting and prediction errors in linear models. When the variables are dummies for age, period, etc. shrinkage is more commonly applied to differences between adjacent parameters, perhaps by fitting cubic splines or piecewise-linear curves (linear splines)...

Maximum likelihood estimation has been the workhorse of statistics for decades, but alternative methods, going under the name “regularization,” are proving to have lower predictive variance. Regularization shrinks fitted values towards the overall mean, much like credibility does. There is...

Bayesian regularization, a relatively new method for estimating model parameters, shrinks estimates towards the overall mean by shrinking the parameters. It has been proven to lower estimation and prediction variances from those of MLE for linear models, such as regression or GLM. It has a...

Parameter shrinkage applied optimally can always reduce error and projection variances from those of maximum likelihood estimation. Many variables that actuaries use are on numerical scales, like age or year, which require parameters at each point. Rather than shrinking these towards zero,...