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Credibility-like Shrinkage in Linear Models for Pricing and Reserving

Venter, Gary

This is an introduction to Bayesian shrinkage in semi-parametric models for actuaries. It starts with a link of the James-Stein estimator to an actuarial estimation approach known as credibility, and shows that by shrinking estimates towards the overall mean, the predictive variance is reduced. Then it argues that ridge regression and lasso achieve a similar improvement in predictive variance also by shrinking estimates towards the overall mean, but now by shrinking regression coefficients. This can be done more simply and directly by a fully Bayesian approach.

Semi-parametric regression can also be simplified by shrinking slope changes of linear splines using the fully Bayesian method. This is illustrated by building curves across parameters of the same type in regression models, some resembling age-period-cohort models.

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More About This Work

Academic Units
School of Professional Studies
Published Here
August 7, 2019
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