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...

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...

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)...

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...

Very similar modeling is done for actuarial models in loss reserving and mortality projection. Both start with incomplete data rectangles, traditionally called triangles, and model by year of origin, year of observation, and lag from origin to observation. Actuaries using these models almost...

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,...

Actuaries use age-period-cohort (APC) models for mortality modeling and general insurance loss reserving. Several recent papers have addressed simultaneously modeling related datasets, such as loss triangles for subsets of a class of business or mortality data across regions. This paper does...

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,...