| Summary: | <b>Background</b>: 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. <b>Objective</b>: 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. <b>Methods</b>: 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. <b>Results</b>: For mortality estimates in small populations, D-spline estimators generally have lower errors than standard P-splines. <b>Conclusions</b>: Using penalties based on demographic information about patterns and variability in rate schedules improves P-spline estimators for small populations. <b>Contribution</b>: 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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