@article{Schmertmann_44_45,
author = {Schmertmann, Carl},
title={{D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties}},
journal = {Demographic Research},
volume = {44},
number = {45},
pages = {1085--1114},
doi = {10.4054/DemRes.2021.44.45},
year = {2021},
abstract = {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. },
URL = {https://www.demographic-research.org/volumes/vol44/45/},
eprint = {https://www.demographic-research.org/volumes/vol44/45/44-45.pdf}
}