Volume 44 - Article 45 | Pages 1085–1114
D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
Background: High-dimensional parametric models with penalized likelihood functions strike a good balance between bias and variance for estimating continuous age schedules from large samples. The penalized spline (P-spline) approach is particularly useful for these purposes, but it in small samples it can often produce implausible age schedule estimates.
Objective: I propose and evaluate a new type of P-spline model for estimating demographic rate schedules. These estimators, which I call D-splines, regularize and smooth high-dimensional splines by using demographic patterns rather than generic mathematical rules.
Methods: I compare P-spline estimates of age-speciﬁc mortality rates to three alternative D-spline estimators, over a large number of simulated small populations with known rates. The penalties for the D-spline estimators are derived from patterns in the Human Mortality Database.
Results: For mortality estimates in small populations, D-spline estimators generally have lower errors than standard P-splines.
Conclusions: Using penalties based on demographic information about patterns and variability in rate schedules improves P-spline estimators for small populations.
Contribution: This paper expands demographers' toolkit by developing a new category of P-spline estimators that are more reliable for estimating mortality in small populations.
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