  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, nearby
parameters are better shrunk towards 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.
