TY  - JOUR
A1  - Schmertmann, Carl
T1  - D-splines: Estimating rate schedules using high-dimensional splines with empirical demographic penalties
Y1  - 2021/06/01
JF  - Demographic Research
JO  - Demographic Research
SN  - 1435-9871
SP  - 1085
EP  - 1114
DO  - 10.4054/DemRes.2021.44.45
VL  - 44
IS  - 45
UR  - https://www.demographic-research.org/volumes/vol44/45/
L1  - https://www.demographic-research.org/volumes/vol44/45/44-45.pdf
L2  - https://www.demographic-research.org/volumes/vol44/45/44-45.pdf
L3  - https://www.demographic-research.org/volumes/vol44/45/files/readme.44-45.txt
L3  - https://www.demographic-research.org/volumes/vol44/45/files/demographic-research.44-45.zip
N2  - 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. 

ER  -