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 toward zero, nearby parameters are better shrunk toward each other. Semiparametric regression is a statistical discipline for building curves across parameter classes using shrinkage methodology. It is similar to but more parsimonious than cubic splines. We introduce it in the context of Bayesian shrinkage and apply it to joint mortality modeling for related populations. Bayesian shrinkage of slope changes of linear splines is an approach to semiparametric modeling that evolved in the actuarial literature. It has some theoretical and practical advantages, like closed-form curves, direct and transparent determination of degree of shrinkage and of placing knots for the splines, and quantifying goodness of fit. It is also relatively easy to apply to the many nonlinear models that arise in actuarial work. We find that it compares well to a more complex state-of-the-art statistical spline shrinkage approach on a popular example from that literature.

最佳应用的参数收缩总是可以减少最大似然估计的误差和投影方差。精算师使用的许多变量都是数字尺度的，例如年龄或年份，这需要每个点的参数。与其将它们缩小到零，不如将附近的参数彼此缩小。半参数回归是一种统计学科，用于使用收缩方法构建跨参数类的曲线。它类似于三次样条，但比三次样条更简洁。我们在贝叶斯收缩的背景下引入它，并将其应用于相关人群的联合死亡率建模。线性样条斜率变化的贝叶斯收缩是精算文献中发展起来的一种半参数建模方法。它具有一定的理论和实践优势，像闭合曲线一样，直接和透明地确定收缩程度和为样条放置节点，以及量化拟合优度。它也相对容易应用于精算工作中出现的许多非线性模型。我们发现它与该文献中一个流行的例子中更复杂的最先进的统计样条收缩方法相比很好。